Resources

Resources

Interpret confidence intervals for population means

Drinkers of Jitterfuel iced tea complain that the amount of caffeine per bottle varies too much. Jitterfuel decided to test these claims by measuring the amount of caffeine in

125

randomly selected bottles from the latest production batch. The company found a

95\%

confidence interval of for the mean amount of caffeine in bottles from the production batch (in milligrams).

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Is the following conclusion valid?

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100

more samples are taken (with elements chosen randomly and independently), it is expected that exactly

100

of them will each produce a

95\%

confidence interval that contains its sample mean.

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Hashtag University is conducting a study to see how much time freshmen spend using social media. The university asked a random sample of

150

freshmen how much time they spend on social media apps per day. Hashtag University calculated a

99\%

confidence interval of for the mean number of hours freshmen spend on social media apps per day.

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Is the following conclusion valid?

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99\%

chance that the mean number of hours freshman at Hashtag University spend on social media apps daily is in the interval .

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A store owner wants to check whether his competitor, Moe's Monster Market, carries larger produce than he does. He purchased

100

randomly selected kiwis from Moe's and weighed them. The owner found a

95\%

confidence interval of for the mean weight of kiwis from Moe's (in grams).

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Is the following conclusion valid?

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100

more samples are taken (with elements chosen randomly and independently), it is expected that exactly

95

of them will each produce a

95\%

confidence interval that contains its sample mean.

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A university is trying to accommodate its commuter students in its course scheduling. In a survey, the school asked a sample of

75

randomly chosen students how long their daily commute is, in minutes. The data showed a

90\%

confidence interval of for the mean commute time for students at the university.

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Is the following conclusion valid?

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100

more surveys are conducted (each using a sample with members chosen randomly and independently), it is expected that exactly

100

of them will each produce a

90\%

confidence interval that contains its sample mean.

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Education officials in Fairview are considering adjustments to the community service requirements for high school graduation. They conducted a survey to assess the typical involvement in volunteering among local high school students. In the survey,

75

randomly chosen Fairview students reported their volunteer hours from the last year. The officials calculated a

95\%

confidence interval of for the mean number of hours Fairview students volunteered last year.

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Is the following conclusion valid?

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If the officials conduct another survey, there is a

95\%

chance that the mean number of hours Fairview students volunteered last year will be in the new survey's

95\%

confidence interval.

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The superintendent of Morristown School District is concerned about the study habits of students in the district. He had guidance counselors throughout the city ask

100

randomly chosen students how many hours they study each day. The superintendent computed a

95\%

confidence interval for the mean number of hours students in Morristown study each day.

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Is the following conclusion valid?

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If Sam takes more same-sized samples, then

95\%

of the students in each sample will study between

2.9

3.3

hours each day.

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A cell phone company is thinking about opening a store in Millersburg. To help the company make a decision, its marketing department conducted a survey about cell phone ownership in the city. A total of

875

randomly chosen Millersburg households participated in the survey. From the survey results, market researchers at the phone company calculated a

95\%

confidence interval of for the mean number of cell phones owned by households in Millersburg.

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Is the following conclusion valid?

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100

more surveys are conducted (each using a sample with members chosen randomly and independently), it is expected that exactly

100

of them will each produce a

95\%

confidence interval that contains its sample mean.

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1

. In a survey of

2035

73 \%

reported working out

3

or more days a week. What is the margin of error? What is the interval that is likely to contain the exact percent of all people who work out

3

or more days a week? Show all work.

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Mean and Mean Absolute Deviation - Quir - Level F

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The dot plot shows the number of students who attended the first five meetings of a school's Math Club.

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Find the mean of the data.

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9

9

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At the next meeting of the club, there are

15

students. How does including this value with the data affect the mean?

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The mean increases from

9

\square

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6

8

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Previous question

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0 / 1

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urrent Attempt in Progress

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Average Penalty Minutes in the NHL An interval estimate was constructed for mean penalty minutes given to NHL players in a seas using data from players on the Ottawa Senators as our sample. Some percentiles from a bootstrap distribution of

5000

sample mean are shown below.

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\begin{tabular}{ccccccccccc}

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0.5 \%

1.0 \%

2.0 \%

2.5 \%

5.0 \%

95.0 \%

97.5 \%

98.0 \%

99.0 \%

0.5 \%

0

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\hline Percentile &

13

7

14

3

15

3

15

6

16

9

32

8

34

4

35

0

36

7

37

8

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Use this information to find a

0.5 \%

1

confidence interval for the mean penalty minutes of NHL players. Assume that the players on this team are a reasonable sample from the population of all players.

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Enter the exact answers.

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0.5 \%

1

confidence interval is

0.5 \%

3

0.5 \%

3

25

25

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eTextbook and Media

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3

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4

. CARBON DATING Carbon

-14

has a decay constant of of thects based on the amount of information

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a. a fossil that has lost

95 \%

14

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b. an animal skeleton that has

95 \%

14

A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found a confidence interval for the mean score to be between

475

521

. What is the margin of error on the survey? Do not write

\pm

on the margin of error.

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Answer:__________

A study was commissioned to find the mean weight of the residents in certain town. The study found the mean weight to be

153

pounds with a margin of error of

5

pounds. Which of the following is not a reasonable value for the true mean weight of the residents of the town?

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148

5

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149

1

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156

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158

5

A study was commissioned to find the mean weight of the residents in certain town. The study found a confidence interval for the mean weight to be between

149

155

pounds. What is the margin of error on the survey? Do not write

\pm

on the margin of error.

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Answer:_________

A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found a confidence interval for the mean score to be between

501

531

. What is the margin of error on the survey? Do not write

\pm

on the margin of error.

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Answer:________

A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found that the mean SAT score was

454

with a margin of error of

17

. Write a confidence interval for the true mean SAT score of the graduating high school seniors.

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(______,______)

A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. The survey reported a confidence interval that between

57.5 \%

60.5 \%

of the residents supports the plan. What is the margin of error on the survey? Do not write

\pm

on the margin of error.

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Answer:________

A study was commissioned to find the mean weight of the residents in certain town. The study found a confidence interval for the mean weight to be between

146

162

pounds. What is the margin of error on the survey? Do not write

\pm

on the margin of error.

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A study was commissioned to find the mean weight of the residents in certain town. The study found a confidence interval for the mean weight to be between

186

200

pounds. What is the margin of error on the survey? Do not write

\pm

on the margin of error.

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A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found a confidence interval for the mean score to be between

519

557

. What is the margin of error on the survey? Do not write

\pm

on the margin of error.

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7

Humboldt penguins at the Green Valley Aquarium are very playful, and visitors love to watch them. The penguins' weights range from

8

5

12

5

pounds. Their mean weight is about

10

4

pounds, and the mean absolute deviation is about

1

2

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What can you conclude from these data and statistics? Select all that apply.

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(A) All of the penguins weigh less than

13

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(B) The weight of the penguins typically varies by about

10

4

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(C) None of the penguins weigh less than

8

5

Find the critical values for a

99 \%

confidence interval using the chi-square distribution with

27

degrees of freedom. Round the answers to three decimal places.

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The critical values are

\square

\square

observing a sample mean of

120m^{34}\alpha=1.0a

, winount of time off lask is convincing evidence that the average amountes. What sample size would you need to estimate the average amount of time spent on non-school related assignments, within

2

minutes if you wanted to be

97\%

confident in your estimate, given

\sigma=9.5

A child psychologist believes that children perform better on tests when they are given perceived freedom of choice. To test this belief, the psychologist carried out an experiment in which third graders were randomly assigned to two groups, A and B. Each child was given the same simple logic test. However, in group B, each child was given the freedom to choose a text booklet from many with various drawings on the covers. The performance of each child was rated as Very Good, Good, and Fair. The results are summarized in the table provided. Test, at the

5

\% level of significance, whether there is sufficient evidence in the data to support the psychologist's belief.

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\begin{tabular}{|l|l|l|l|}

\newline

\hline \multicolumn{

2

}{c}{} & \multicolumn{

2

}{c|}{ Group } \\

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\hline \multicolumn{

2

}{|c|}{ A } & B \\

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\hline \multirow{

2

}{*}{\begin{tabular}{l}

\newline

\newline

\end{tabular}} & Very Good &

32

29

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2

4

55

51

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2

4

10

13

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Hannah tried to find the derivative of

-3+8 x

using basic differentiation rules. Here is her work:

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\frac{d}{d x}(-3+8 x)

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1=\frac{d}{d x}(-3)+\frac{d}{d x}(8 x)

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2=0+\frac{d}{d x}(8 x)

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3=\frac{d}{d x}(8) \frac{d}{d x}(x)

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4=0 \cdot 1

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5=0

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At which step did Hannah make a mistake, if at all?

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1

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1

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2

\newline

3

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(D) Hannah did not make a mistake

2018

, the Pew Internet \& American Life Project asked

743

13

17

several questions about their attitudes toward social media. The results showed that

602

say social media makes them feel more connected to what is going on in their friends' lives;

513

say social media helps them interact with a more diverse group of people; and

275

feel pressure to post content that will get a lot of likes and comments.

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Round your answers to four decimal places.

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a. Develop a point estimate of the proportion of teens aged

13

17

who say social media makes them feel more connected to what is going on in their friends' lives.

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b. Develop a point estimate of the proportion of teens aged

13

17

who say social media helps them interact with a more diverse group of people.

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c. Develop a point estimate of the proportion of teens aged

13

17

who feel pressure to post content that will get a lot of likes and comments.

70 L+60 S<5,600

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0.02 L+0.01 S \leq 2.5

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Members of the swim team want to wash their hair. Each short-haired member requires the same number of liters of water and soap, and each long-haired member requires the same number of liters of water and soap. The bathroom has less than

5

600

liters of water and at most

2

5

liters of shampoo. The system of inequalities shown, where

S

represents the number of short-haired members and

L

the number of long-haired members, describes this situation. Does the bathroom have enough water and shampoo for

8

long-haired members and

7

short-haired members?

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1

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(A) The bathroom has enough water and shampoo.

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(B) The bathroom has enough water but not enough shampoo.

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(C) The bathroom has enough shampoo but not enough water.

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(D) The bathroom has neither enough water nor enough shampoo.

Surya gave each member of his family a different playlist of random song to listen to and asked them to rank each song between

0

10

. He compared his family's rankings with the release year of each song and created the following scatter plot and trend line. Assuming the line correctly models the trend in the data, what does this line's slope of

-0

096

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1

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(A) The difference in ratings for rock songs and rap songs was

-0

096

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B The difference in ratings for rock songs and country songs was

-0

096

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(C) On average, each

1

year increase in release year was associated with a

-0

096

point change in score.

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(D) On average, each

1

point increase in score was associated with a

An astronomer observes the velocity of a galaxy at a distance of

100

megaparsecs to calculate its distance two billion years from now using two different models. In the first model, the distance from the galaxy to Earth increases by

9\,\text{MPC}

every billion years. In the second model, the distance from the galaxy to Earth increases by

10

percent every billion years. Two billion years from now, how much further would the galaxy be in the second model compared to the first model in megaparsecs?

2147

adults in a recent year,

1400

say they have made a New Year's resolution.

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90 \%

95 \%

confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.

5

1

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Suppose heights of seasonal pine saplings are normally distributed and have a known population standard deviation of

22

millimeters and an unknown population mean. A random sample of

21

saplings is taken and gives a sample mean of

286

millimeters. Find the confidence interval for the population mean with a

99 \%

confidence level.

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\begin{tabular}{lllll}

\newline

\mathbf{z}_{0.10}

\mathbf{z}_{0.05}

\mathbf{z}_{0.025}

\mathbf{z}_{0.01}

\mathbf{z}_{0.005}

\newline

1

282

1

645

1

960

2

326

2

576

\newline

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You may use a calculator or the common

z

\newline

- Round all numbers to three decimal places, if necessary.

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Provide your answer below:

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The number of square feet per house are normally distributed with a population standard deviation of

154

square feet and an unknown population mean. If a random sample of

16

houses is taken and results in a sample mean of

1550

square feet, find a

80 \%

confidence interval for the population mean.

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\begin{tabular}{ccccc}

\newline

z_{0.10}

z_{0.05}

z_{0.025}

z_{0.01}

z_{0.005}

\newline

1

282

1

645

1

960

2

326

2

576

\newline

\newline

\newline

You may use a calculator or the common

z

\newline

- Round each number to three decimal places.

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Provide your answer below:

The mean age when smokers first start is

13

years old with a population standard deviation of

1

9

years. A researcher thinks that smoking age has significantly changed since the invention of ENDS-electronic nicotine delivery systems. A survey of smokers of this generation was done to see if the mean age has changed. The sample of

31

smokers found that their mean starting age was

12

1

years old. Do the data support the claim at the

1 \%

significance level?

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What are the correct hypotheses?

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\mathrm{H}_{0}:

Select an answer

\vee ? \vee

\newline

\mathrm{H}_{1}

: Select an answer

\vee ? \vee

\newline

Based on the hypotheses, find the following:

\newline

\mathrm{z}=

(Give answer to at least

4

decimal places)

\newline

=

(Give answer to at least

4

decimal places)

\newline

Based on the above we choose to Select an answer

\newline

The correct summary would be: Select an answer that the mean age smokers first start is different than

13

. that the claim

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Question Help: Read

\newline

Submit Question

The mean age when smokers first start is

13

years old with a population standard deviation of

1

9

years. A researcher thinks that smoking age has significantly changed since the invention of ENDS-electronic nicotine delivery systems. A survey of smokers of this generation was done to see if the mean age has changed. The sample of

31

smokers found that their mean starting age was

12

1

years old. Do the data support the claim at the

1 \%

significance level?

\newline

What are the correct hypotheses?

\newline

\mathrm{H}_{0}

: Select an answer

\vee ? \vee

\newline

\mathrm{H}_{1}

: Select an answer

\vee ? \vee \square

\newline

Based on the hypotheses, find the following:

\newline

\mathrm{z}=

(Give answer to at least

4

decimal places)

\newline

p

=

(Give answer to at least

4

decimal places)

\newline

Based on the above we choose to Select an answer

\newline

The correct summary would be: Select an answer that the mean age smokers first start is different than

13

. that the claim

\newline

Question Help: Read

\newline

Submit Question

The mean age when smokers first start is

13

years old with a population standard deviation of

1

9

years. A researcher thinks that smoking age has significantly changed since the invention of ENDS-electronic nicotine delivery systems. A survey of smokers of this generation was done to see if the mean age has changed. The sample of

31

smokers found that their mean starting age was

12

1

years old. Do the data support the claim at the

1 \%

significance level?

\newline

What are the correct hypotheses?

\newline

\mathrm{H}_{0}:

Select an answer

\vee ? \vee \square

\newline

\mathrm{H}_{1}

: Select an answer

\vee ? \vee \square

\newline

Based on the hypotheses, find the following:

\newline

z=

(Give answer to at least

4

decimal places)

\newline

\mathrm{p}

=\square

(Give answer to at least

4

decimal places)

\newline

Based on the above we choose to Select an answer

\newline

The correct summary would be: Select an answer that the mean age smokers first start is different than

13

. that the claim

\newline

Question Help: Rif Read

\newline

Submit Question

1

. An IQ test was given to a simple random sample of

75

students at a certain college. The sample mean score was

105

2

. Scores on this test are known to have a standard deviation of

\sigma=10

. It is desired to construct a

90 \%

confidence interval for the mean IQ score of students at this college.

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a. What is the (point estimate?)

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b. Find the critical value.

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c. Find the standard error.

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d. Find the margin of error.

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e. Construct the

90 \%

confidence interval.

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f. Is it likely that the population mean

\mu

is greater than

100

1

. An IQ test was given to a simple random sample of

75

students at a certain college. The sample mea score was

105

2

. Scores on this test are known to have a standard deviation of

\sigma=10

. It is desired to construct a

90 \%

confidence interval for the mean IQ score of students at this college.

\newline

\newline

a. What is the (point estimate?)

\newline

b. Find the critical value.

\newline

c. Find the standard error.

\newline

d. Find the margin of error.

\newline

e. Construct the

90 \%

confidence interval.

\newline

f. Is it likely that the population mean

\mu

is greater than

100

20

20

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Select the best answer for the question.

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20

. A firm's net income is

\$ 120,000

\$ 12

million. Average assets for the period were

\$ 5

million. For the year,

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1 \%

2

4

\mathrm{ROI}

2.4 \%

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6 \%

1

5

6 \%

\newline

4 \%

1

2

4.8 \%

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\$ 12

0

1

2

6 \%

Mason is working two summer jobs, making

\$7

per hour babysitting and making

\$10

per hour clearing tables. In a given week, he can work at most

12

total hours and must earn no less than

\$90

x

represents the number of hours babysitting and

y

represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.

1

2

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0

1

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A genetic experiment with peas resulted in one sample of offspring that consisted of

447

152

\newline

90 \%

confidence interval to estimate of the percentage of yellow peas.

\newline

b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that

25 \%

of the offspring peas would be yellow

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90 \%

confidence interval. Express the percentages in decimal form

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\square<p<\square

(Round to three decimal places as needed)

It always takes Zach approximately

5

minutes longer to arrive than he says. If Zach says he will arrive in

x

minutes, which of the following functions correctly models the approximate number of minutes it actually takes Zach to arrive?

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment,

16

subjects had a mean wake time of

103.0\,\text{min}

. After treatment, the

16

subjects had a mean wake time of

81.1\,\text{min}

and a standard deviation of

21.3\,\text{min}

. Assume that the

16

sample values appear to be from a normally distributed population and construct a

90\%

confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of

103.0\,\text{min}

before the treatment? Does the drug appear to be effective?

\newline

90\%

confidence interval estimate of the mean wake time for a population with the treatment.

\newline

\text{min} < \mu < \square\,\text{min}

\newline

(Round to one decimal place as needed.)

516

human resource professionals,

45.7\%

said that body piercings and tattoos were big personal grooming red flags. Complete parts (a) through (c) below.

\newline

516

human resource professionals who were surveyed, how many of them said that body piercings and tattoos were big personal grooming red flags?

\newline

236

(Round to the nearest integer as needed.)

\newline

(b). Construct a

99\%

confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big personal grooming red flags.

\newline

0.401 < p < 0.514

\newline

(Round to three decimal places as needed.)

\newline

(c). Repeat part (b) using a confidênce level of

80\%

\newline

< p <

\newline

(Round to three decimal places as needed.)

A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of

40

students in the high school and found a mean of

185

messages sent per day with a standard deviation of

87

messages. At the

95 \%

confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write

\pm

\newline

A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of

52

students in the high school and found a mean of

194

messages sent per day with a standard deviation of

57

messages. At the

95 \%

confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write

\pm

\newline

A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of

92

students in the high school and found a mean of

194

messages sent per day with a standard deviation of

63

messages. At the

95 \%

confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write

\pm

\newline

A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of

74

students in the high school and found a mean of

190

messages sent per day with a standard deviation of

99

messages. Determine a

95 \%

confidence interval for the mean, rounding all values to the nearest whole number.

A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of

36

students in the high school and found a mean of

156

messages sent per day with a standard deviation of

61

messages. Determine a

95

% confidence interval for the mean, rounding all values to the nearest whole number.

40

randomly selected captive extit{Octopus vulgaris}, researchers found that the octopuses could learn to integrate visual and tactile information to find food after a mean of

119

trials. The estimate had a margin of error of

18

95\%

confidence level. Which of the following is the most reasonable conclusion about the number of trials it would take all captive extit{Octopus vulgaris} in general to learn to find the food?

Rock Hill Relaxation Company sells vitamin supplements. They have collected the following budget information about the

10,000

bottles of supplements they expect to sell; Total Direct Material Cost

\$27,000

, Total Direct Labor Cost

\$15,000

, Total Manufacturing Overhead Cost

\$12,000

, Total Selling and Administrative Expenses

\$3,000

. Rock Hillis desired profit is a

50\%

return on investment of their

\$90,000

of total assets.

\newline

At what amount should Rock Hill price its supplements, if they are using the Product Cost Method of pricing?

\newline

\$5.30

\newline

\$10.70

\newline

\$15.75

\newline

\$27,000

0