Interpret confidence intervals for population means

NAME\newline\quad\newlineDATE\newline\quad\newlinePERIOD\newline\quad\newlineLesson 77 Homework Practice\newlineTheoretical and Experimental Probability\newlineThe table shows the results of an experiment in which a spinner was spun 5050 times. Find the experimental probability of each outcome.\newline\newlineP( less than 4)P(\text{ less than } 4)\newline\newlineNumber\newlineFrequency\newlineNumber\newlineFrequency\newline\newline11\newline||\newline||\newline99\newline||\newline||\newline\newline\quad11\newline||\newline\quad33\newline||\newline\newline\quad55\newline||\newline\quad77\newline\quad88\newline\newline\quad99\newline||\newline||\newline\quad22\newline||\newline||\newline\newline\quad55\newline||\newline||\newline\quad88\newline||\newline||\newline\newline505011\newline||\newline505033\newline||\newline\newline505055\newline||505077\newline505088\newline||\newline\newlineP( less than 4)P(\text{ less than } 4)00\newline||\newlineP( less than 4)P(\text{ less than } 4)22\newline||\newline\newlineThe table on the right shows the type and number of businesses in Wilsonville. If there are \newlineP( less than 4)P(\text{ less than } 4)44 businesses in the nearby town of Newberry, predict how many of each type of business there would be in Newberry.\newline55. grocery stores\newline66. retail stores\newline77. restaurants\newline88. pet shops and copy shops\newline\newlineBusiness Type\newlineNumber\newline\newlineGrocery Store\newline\quad33\newline\newlineRetail Store\newlineP( less than 4)P(\text{ less than } 4)66\newline\newlineCopy Shop\newline505011\newline\newlineRestaurant\newlineP( less than 4)P(\text{ less than } 4)88\newline\newlineCar Dealership\newline\quad55\newline\newlinePet Shop\newline\quad33\newline\newlineThe table shows the results of a survey conducted by a local restaurant of some of its customers. The customers were asked what new menu item they would prefer to see added to the menu from the choices provided.\newline\newlineRestaurant Survey\newline\newlineItem\newline\newlineChicken\newline\newlineCarbonara\newline\newlineBeef Tips\newline\newlineShrimp\newline\newlineScampi\newline\newline\newline\newlineNumber of\newline\newlineResponses\newline\newline1111\newline1122\newline1133\newline\newlineWhat is the probability of beef tips being the preferred new menu item?\newlineOut of a similar group of 1144 customers, predict how many would choose beef tips as their preferred new menu item?\newlineOut of a similar group of 1155 customers, predict how many more customers will prefer chicken carbonara to shrimp scampi?\newlineMelinda purchased a snack-size roll of candy tarts, and found that only \newline1166 of them were grape-flavored. Suppose Melinda later buys a king-size roll of candy tarts that contains P( less than 4)P(\text{ less than } 4)88 pieces. How many of that roll can she expect to be grape-flavored?\newlineA soccer coach is dividing his players into groups of five. Kate, Jocilyn, Monty, Giorgianna, and Henry are in one group. Each one of their names is written on a separate piece of paper. The coach draws a name each week (and then replaces it for the next week) to find the group leader.\newline1313. Predict the number of times that Giorgianna's name will be drawn in 1188 weeks. Round to the nearest whole number.\newline1414. Kate's name was actually drawn P( less than 4)P(\text{ less than } 4)00 times during the 1188-week period. What was the experimental probability that Kate's name was drawn, and how does it compare to the theoretical probability?\newlineMath Accelerated - Chapter 1010 Statistics and Probability
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The sitting height of a person is the vertical dislance between the sitting surface and the top of the head. The accompanying table lists sitting heights (mm) of randomly selected U.S. Army personnel collected as part of a large reputable study Using the data with a 00.0505 significance level, what do you conclude?\newline(i) Click the icon to view the sitting height data\newlineFirst test for an interaction between the two factors. Determine the null and alternative hypotheses Choose the correct answer below.\newlineA. H0 \mathrm{H}_{0} : Sitting heights are not affected by gender. H1 \mathrm{H}_{1} : Sitting heights are affected by gender:\newlineB. H0 \mathrm{H}_{0} . Sitting heights are affected by an interaction between gender and handedness: H1 \mathrm{H}_{1} Sitting heights are not affected by an interaction between gender and handedness.\newlinec. H0 \mathrm{H}_{0} . Sitting heights are not affected by handedness. H1 \mathrm{H}_{1} Sitting heights are affected by handedness.\newlineD. H0 \mathrm{H}_{0} : Sitting heights are not affected by an interaction between gender and handedness.\newlineH \mathrm{H}_{\text {. }} . Sitting heighis are affected by an interaction between gender and handedness\newlineSitting Height Data\newline\begin{tabular}{|l|c|c|}\newline\hline & Right-Handed & Left-Handed \\\newline\hline Female & 858879875787897858879875787897 & 872858884845813872858884845813 \\\newline\hline Male & 943907903914945943907903914945 & 1001916103191597610019161031915976 \\\newline\hline\newline\end{tabular}
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Case study 33\newlineScreening for Antibody to the Human Immunodeficiency Virus\newlineBackground:\newlineIn December 19821982, a report in the MMWR described three persons who had developed acquired immunodeficiency syndrome (AIDS) but who had neither of the previously known risk factors for the disease: homosexual/bisexual activity with numerous partners and intravenous drug use. These three persons had previously received whole-blood transfusions.By 19831983, widespread recognition of the problem of transfusion-related AIDS led to controversial recommendations that persons in known high-risk groups voluntarily defer from donating blood.\newlineIn June 19841984, after the discovery of the human immunodeficiency virus (HIV), five companies were licensed to produce enzyme-linked immunosorbent assay (EIA, then called ELISA) test kits for detecting HIV antibody. Blood bank directors were anxiously waiting to start screening blood with the new test until March 22, 19851985, the date the first test kit was approved by the FDA.\newlinePART I\newlineTo help in the discussions, the State Epidemiologist turns to pre-licensure information regarding the sensitivity and specificity of EIA. The information indicates that the sensitivity of EIA is 95.0%95.0\% (0.95)(0.95) and the specificity is 98.0%98.0\% (0.98)(0.98).\newlineQuestion11a : With this information, by constructing a 22-by-22 table, calculate the predictive-value positive and predictive-value negative of the EIA in a hypothetical population of 1,000,0001,000,000 blood donors. Assume that the actual prevalence of HIV antibody among blood donors is 0.04%0.04\% (0.0004)(0.0004).\newlineQuestion11b: Using a separate 22-by-22 table, calculate predictive-value positive and predictive-value negative for a population of (0.95)(0.95)11 drug users. Assume that the actual prevalence of HIV antibody among intravenous drug users is (0.95)(0.95)22 (0.95)(0.95)33.\newlineQuestion 22a: Do you think that the EIA is a good screening test for the blood bank? What would you recommend to the blood bank director about notification of EIA-positive blood donors?\newlineQuestion 22b: Do you think that the EIA performs well enough to justify informing test-positive clients in the drug abuse clinics that they are positive for HIV?\newlineQuestion 33: If sensitivity and specificity remain constant, what is the relationship of prevalence to predictive-value positive and predictive-value negative?
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Toby rides his bike to school every day and to his best friend's house regularly. One week, he rode to and from school 55 times and to and from his best friend's house 33 times. He rode a total of 14.414.4 miles that week. The next week, he rode to and from school 44 times and to and from his best friend's house 66 times. He rode a total of 14.414.4 miles that week, too.\newlineThis system of equations can be used to represent the situation:\newline5x+3y=14.45x + 3y = 14.4\newline4x+6y=14.44x + 6y = 14.4\newlineWhich statement is correct?\newlineChoices:\newline(A)In the system of equations, xx represents the total distance Toby traveled to and from school each week, and yy represents the total distance he traveled to and from his best friend's house each week.\newline(B)In the system of equations, xx represents the round-trip distance to and from Toby's best friend's house, and yy represents the round-trip distance to and from Toby's school.\newline(C)In the system of equations, xx represents the round-trip distance to and from Toby's school, and yy represents the round-trip distance to and from his best friend's house.\newline(D)In the system of equations, xx represents the total distance Toby traveled to and from his best friend's house each week, and yy represents the total distance he traveled to and from his school each week.\newlineWhat was the total distance Toby traveled to and from school the first week?\newline____ miles\newline
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The following data represent the pH \mathrm{pH} of rain for a random sample of 1212 rain dates. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Complete parts (a) through (d) below.\newline\begin{tabular}{llll}\newline55.0505 & 55.7272 & 44.6262 & 44.8080 \\\newline55.0202 & 44.5757 & 44.7474 & 55.1919 \\\newline44.6161 & 44.7676 & 44.5656 & 55.3030\newline\end{tabular}\newline(a) Determine a point estimate for the population mean.\newlineA point estimate for the population mean is \square (Round to two decimal places as needed.)\newline(b) Construct and interpret a 9595\% confidence interval for the mean pH \mathrm{pH} of rainwater. Select the correct choice below and fill in the answer boxes to complete your choice.\newline(Use ascending order. Round to two decimal places as needed.)\newlineA. There is a 95% 95 \% probability that the true mean pH \mathrm{pH} of rain water is between \square and \square \newlineB. If repeated samples are taken, 95% 95 \% of them will have a sample pH \mathrm{pH} of rain water between \square and \square \newlineC. There is 95% 95 \% confidence that the population mean pH \mathrm{pH} of rain water is between \square and \square \newline(c) Construct and interpret a 9999\% confidence interval for the mean pH \mathrm{pH} of rainwater. Select the correct choice below and fill in the answer boxes to complete your choice.\newline(Use ascending order. Round to two decimal places as needed.)\newlineA. There is a \square 66 probability that the true mean pH \mathrm{pH} of rain water is between \square and \square .\newlineB. There is \square 66 confidence that the population mean pH \mathrm{pH} of rain water is between \square and \square \newlineC. If repeated samples are taken, \square 66 of them will have a sample pH \mathrm{pH} of rain water between \square and \square
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Start Spring 20242024\newlineQuestion 55,\newlineHW Score: 73.89% 73.89 \% ,\newline88.11.1717-T\newline44.4343 of 66 points\newlinePart 44 of 44\newlinePoints: 00.55 of 11\newlineSave\newlineA simple random sample of size n=10 n=10 is obtained from a population with μ=63 \mu=63 and σ=15 \sigma=15 .\newline(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of xˉ \bar{x} .\newline(b) Assuming the normal model can be used, determine P(xˉ<66.4) \mathrm{P}(\bar{x}<66.4) .\newline(c) Assuming the normal model can be used, determine P(x64.2) P(x \geq 64.2) .\newline(a) What must be true regarding the distribution of the population?\newlineA. The sampling distribution must be assumed to be normal.\newlineB. Since the sample size is large enough, the population distribution doe need to be normal.\newlineC. The population must be normally distributed and the sample size must be large.\newlineD. The population must be normally distributed.\newlineAssuming the normal model can be used, describe the sampling distribution xˉ \bar{x} . Choose the correct answer below.\newlineA. Normal, with μxˉ=63 \mu_{\bar{x}}=63 and σxˉ=15 \sigma_{\bar{x}}=15 \newlineB. Normal, with μxˉ=63 \mu_{\bar{x}}=63 and n=10 n=10 11\newlineC. Normal, with μxˉ=63 \mu_{\bar{x}}=63 and n=10 n=10 33\newline(b) n=10 n=10 44 (Round to four decimal places as needed.)\newline(c) n=10 n=10 55 (Round to four decimal places as needed.)
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FSPotW Week 33 (1111).PNG\newlineFuneral Services Problem of the Week\newlineInvoice\newlineYou're about to give the following invoice\newlineNVOICENO: 123456123456\newlineDATE:\newlineto a customer, but the\newlinecomputer has been giving weird totals lately\newline\newlineP.O. NUMBER\newlineTERMS\newlinePROJECT\newline\newline\newlineThe computer says that this customer owes \newline$5,068.13\$5,068.13.\newlineExplain at least two places where the computer could have made a mistake.\newlineSupport your answer with numbers from\newlineBill to:\newlineMr. customer 13001300 Goodceal Lane New Orleans, LA 7011370113\newlineML\newlineIR\newlineMinx Le...\newlineIsaac Ra.\newlineKT\newlineCamerón...\newlineKeshawt\newlineJG\newlineKT\newline\newlineQUANTITY\newlineRATE\newlineAMOUNT\newline\newline11\newlineTransportation (hearse)\newline$50.00\$50.00\newline$50.00\$50.00\newline\newline11\newlineGravesite\newline$2,345.25\$2,345.25\newline$2,345.25\$2,345.25\newline\newline11\newlineFieldstone - 1818 Gauge Steel Casket\newline$1,095.00\$1,095.00\newline$1,095.00\$1,095.00\newline\newline11\newlineTax\newline$76.65\$76.65\newline$76.65\$76.65\newline\newline88\newlineFlower Arrangements\newline$25.50\$25.50\newline$50.00\$50.0000\newline\newline99.2525\newlineHourly staff\newline$50.00\$50.0011\newline$50.00\$50.0022\newline\newline11\newlinePartial refund on gravesite from town\newline($50.00\$50.0033)\newline($50.00\$50.0033)\newline\newline6060\newlineMemorial printed cards\newline$50.00\$50.0055\newline$50.00\$50.0066\newline\newline55\newlineEmbalming\newline$50.00\$50.0077\newline$50.00\$50.0088\newline\newline\newlinethe invoice.
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DeltaMath\newline\leftarrow Back to Home\newline44/1919 Basics of Polar Coordinates\newlineDue: April 2626 at 1111:5959 PM\newlineGrade: \newline6767%\newline\checkmark Polar Coordinates to Rectangular Form\newline\checkmark Rectangular Coordinates to Polar Form\newline\checkmark Graphing Polar Curves\newline\checkmark Tangent Lines to Polar Curves\newlineInterpreting Polar Derivatives\newlineAbsolute Extreme Values in Polar\newlineCalculator\newlineTroy Martinez\newlineLog Out\newlineInterpreting Polar Derivatives\newlineScore: \newline00//55\newlinePenalty: none\newlineQuestion\newlineShow Examples\newlineA curve is described by the equation in polar coordinates \newliner=2cosθr=2\cos \theta. Determine \newliney(θ)y(\theta) and \newlinedydθ\frac{dy}{d\theta} when \newlineθ=4π3\theta=\frac{4\pi}{3} and answer the analysis question below. Write your answers as exact values or rounded to three decimal places.\newlineAnswer Attempt 11 out of 22\newliney(θ)=(4π3),= dydθ=,dydθθ=4π3= "Based on the above information, the curve is moving ", the undefined when θ=4π3:\begin{array}{l} y(\theta)\quad=\square\left(\frac{4\pi}{3}\right),=\square \ \frac{dy}{d\theta}\quad=\square,\left.\frac{dy}{d\theta}\right|_{\theta=\frac{4\pi}{3}}=\square \ \text{"Based on the above information, the curve is moving "},\overrightarrow{\text{ the }} \text{ when }\theta=\frac{4\pi}{3}: \end{array}\newlineBased on the above information, the curve is moving the when \newlineθ=4π3\theta=\frac{4\pi}{3} since \newline\checkmark11\newline\checkmark22 \newline\checkmark11\newlineSubmit Answer
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\therefore DeltaMath\newline \leftarrow Back to Home\newline44/1919 Basics of Polar Coordinates\newlineDue: April 2626 at 1111:5959 PM\newlineGrade: 67% 67 \% \newline \checkmark Polar Coordinates to Rectangular Form\newline \checkmark Rectangular Coordinates to Polar Form\newline \checkmark Graphing Polar Curves\newline \checkmark Tangent Lines to Polar Curves\newlineInterpreting Polar Derivatives\newlineAbsolute Extreme Values in Polar\newlineCalculator\newlineTroy Martinez\newlineLog Out\newlineInterpreting Polar Derivatives\newlineScore: 0/5 0 / 5 \newlinePenalty: none\newlineQuestion\newlineShow Examples\newlineA curve is described by the equation in polar coordinates r=2cosθ r=2 \cos \theta . Determine y(θ) y(\theta) and \leftarrow 00 when \leftarrow 11 and answer the analysis question below. Write your answers as exact values or rounded to three decimal places.\newlineAnswer Attempt 11 out of 22\newliney(θ)=(4π3)=dydθ=dydθθ=4π3= \begin{array}{lll} y(\theta) & =\square\left(\frac{4 \pi}{3}\right)=\square \\ \frac{d y}{d \theta} & =\square & \left.\frac{d y}{d \theta}\right|_{\theta=\frac{4 \pi}{3}}=\square \end{array} \newline \leftarrow 22\newline \leftarrow 22\newlineBased on the above information, the curve is moving \leftarrow 22 the \leftarrow 22 when \leftarrow 11 since \leftarrow 22\newline \leftarrow 88 \leftarrow 22\newlineSubmit Answer
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