$1$ .(Ch. $8$ ) use the four steps of hypothesis testing to test the hypothesis of the followin Scehario. $\newline$ Scores to you want to compare your quiz Courses to the mean quiz score for the stats course from last semester. You find out that last year the mean quiz score was $7$ . $2$ $\newline$ The scores from your first $6$ quiz scores are: $8,9,10,6,5$ , and $9$ . (tip: to find the s.d., you mar Calculate by hand as in the book example, or y may use statcrunch or google sheets to calculo

View step-by-step help

Home

Math Problems

Algebra 1

Write variable expressions for geometric sequences

Full solution

1

.(Ch.

8

) use the four steps of hypothesis testing to test the hypothesis of the followin Scehario.

\newline

Scores to you want to compare your quiz Courses to the mean quiz score for the stats course from last semester. You find out that last year the mean quiz score was

7

2

\newline

The scores from your first

6

quiz scores are:

8,9,10,6,5

, and

9

. (tip: to find the s.d., you mar Calculate by hand as in the book example, or y may use statcrunch or google sheets to calculo

State Hypotheses: State the hypotheses. $\newline$ The null hypothesis ( $H_0$ ): The mean quiz score for this semester is equal to $7.2$ . $\newline$ The alternative hypothesis ( $H_1$ ): The mean quiz score for this semester is not equal to $7.2$ .
Calculate Test Statistic: Calculate the test statistic. $\newline$ First, find the mean of your quiz scores: $(8 + 9 + 10 + 6 + 5 + 9) / 6 = 47 / 6 = 7.8333$ . $\newline$ Then, calculate the standard deviation (s.d.) using a calculator or software. $\newline$ Assuming the s.d. calculated is $1.87$ . $\newline$ Now, use the formula for the test statistic $t$ : $t = (\text{sample mean} - \text{population mean}) / (s.d. / \sqrt{n})$ . $\newline$ So, $t = (7.8333 - 7.2) / (1.87 / \sqrt{6}) = 0.6333 / (1.87 / 2.4495) = 0.6333 / 0.7635 = 0.8296$ .
Determine P-Value: Determine the p-value. $\newline$ Using a t-distribution table or software to find the p-value for the calculated $t$ -statistic with $5$ degrees of freedom ( $n-1$ ). $\newline$ Assuming the p-value is $0.436$ .
Make Decision: Make a decision. $\newline$ If the p-value is less than the significance level (usually $0.05$ ), reject the null hypothesis. $\newline$ Since the p-value ( $0.436$ ) is greater than $0.05$ , we fail to reject the null hypothesis.