Exam 20: Inferences About Means

A manufacturer claims that the mean amount of juice in its $473 \mathrm {~mL}$ bottles is 476 mL.A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this.The hypotheses are: H0: ? = 476 mL HA: ? < 476 mL Explain the result of a Type I error.

A researcher performs a hypothesis test to test the claim that among car owners in one town,the mean number of kilometres driven per year is greater than 22,540.Use the provided computer output to draw a conclusion about the number of miles driven at a significance level of 0.01. Test of $\mathrm { H } _ { 0 }$ : ? = 22,540 vs $\mathrm { H } _ { \mathrm { A } }$ : ? > 22,540 N Mean StDev t P-value 26 25,270 6750 2.06 0.025

Quality control engineers are trying to improve the number of unpopped kernels in their company's microwave popcorn.Changes to the oil have recently been made,so the engineers are testing the hypothesis $\mathrm { H } _ { 0 }$ : ? = 25 against $\mathrm { H } _ { \mathrm { A } }$ : ? < 25.