Activity 2:Relating confidence intervals to hypothesis testing.

A survey was administered in Atlanta, GA to learn about commuting habits.500 respondents answered the question: how long is your daily commute in minutes?The data is on StatKey under bootstrap confidence intervals for a single mean.

1.Use StatKey to calculate a 98% confidence interval using the percentile method.

2.Interpret the confidence interval you calculated.

3.If we planned to use this confidence interval to determine the decision for a two-sided hypothesis test, what significance level would we use for the hypothesis test?

4.Now, using that significance level and your confidence interval as a guide, which of the below hypothesis tests would have a significant result? (there may be more than one that would be significant).

A.H₀: mu = 30versusH_a:mu not equal 30

B.H₀: mu = 26versusH_a:mu not equal 26

C.H₀: mu = 32versusH_a:mu not equal 32

D.H₀: mu = 31versusH_a:mu not equal 31

E.H₀: mu = 28versusH_a:mu not equal 28

5.Assume a different researcher collected 500 commute times in Philadelphia with the intent of testing the below hypotheses:

H₀: mu = 20versusH_a:mu >20

The p-value for her test was 0.006.

a.What is the conclusion for her test, both generic and in context?

b.Where was the center of the randomization distribution she used to calculate the p-value?

c.Based on the same sample, she calculates a 95% confidence interval.Which of the statements below must be TRUE?

i.20 is a value in the confidence interval

ii. The confidence interval is entirely larger than the value 20, for example (22 to 28)

iii.The confidence interval is entirely smaller than the value 20, for example (14 to 19).