9. Hypothesis Testing for One Sample

A teacher claims her students’ average test score is 75. A researcher suspects it’s different. A sample of 25 students has a mean score of 78 with a standard deviation of 6.

$\left(A\right)$ Create a $90\%$ confidence interval for the mean test score.

A teacher claims her students’ average test score is 75. A researcher suspects it’s different. A sample of 25 students has a mean score of 78 with a standard deviation of 6.

$\left(B\right)$ At the $0.10$ significance level, test the claim.

Graphical Analysis In Exercises 57–60, you are given a null hypothesis and three confidence intervals that represent three samplings. Determine whether each confidence interval indicates that you should reject H0. Explain your reasoning.

Graphical Analysis In Exercises 57–60, you are given a null hypothesis and three confidence intervals that represent three samplings. Determine whether each confidence interval indicates that you should reject H0. Explain your reasoning.

Graphical Analysis In Exercises 57–60, you are given a null hypothesis and three confidence intervals that represent three samplings. Determine whether each confidence interval indicates that you should reject H0. Explain your reasoning.

In Exercises 5–16, use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal.

The Freshman 15 The “Freshman 15” refers to the belief that college students gain 15 lb (or 6.8 kg) during their freshman year. Listed below are weights (kg) of randomly selected male college freshmen (from Data Set 13 “Freshman 15” in Appendix B). The weights were measured in September and later in April.

b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)?