1. Conductivity is measured in terms of watts of heat power transmitted per square meter of surface per degree Celsius of temperature difference on the two sides of the material. In these units, glass has conductivity about 1. The National Institute of Standards and Technology provides exact data on properties of materials. Here are 11 measurements of the heat conductivity of a particular type of glass.

1.11 1.07 1.11 1.07 1.12 1.08 1.08 1.18 1.18 1.18 1.12

Is there evidence that the conductivity of this type of glass is greater than 1? Carry out an appropriate test and then give an interval estimate of the mean conductivity.

2. For a sample of size 5, a test of the null hypothesis vs a two-sided alternative gives t = 2.45.

A. Is the test result significant at the 5% level?

B. Now assume that the same test statistic was obtained for a sample size of n = 10. Is the test result significant at the 5% level? How did the statistical significance change with the sample size?

3. The city manager measures response times by looking at the proportion of calls for which paramedics arrived within 8 minutes. Last year, paramedics arrived on scene 75% of the time within 8 minutes. The city manager wants to determine whether they have done significantly better this year.

A. State appropriate null and alternative hypotheses for the city manager to test.

B. Describe a Type I and Type II error in this setting.

C. Explain the consequences of each type of error.

D. Which is more serious: a Type I error or a Type II error? Justify your answer

4. A one-sided test of the null hypothesis versus the alternative has power equal to 0.5. Will the power for the alternative be higher or lower than 0.5? Justify your answer.