Question

a). The distribution of all _____ proportions is denoted by P ̂. ( ) A population B sample C random D observed

b). Aviation experts fear that pilots are being asked to fly longer than is recommended by national guidelines. Current FAA regulations for domestic flights generally limit pilots to eight hours of flight time during a 24-hour period. FAA administrators conduct an analysis using a large sample of flight records for domestic flights in the past year. The average flight time is found to be 8.21hours. What are the null and alternative hypotheses appropriate for this test? ( )

A H_0: μ=8 H_A: μ<8

B H_0: μ=8 H_A: μ≠8

C H_0: μ=8. H_A: μ>8

D H_0: μ=8.21 H_A: μ<8.21

E H_0: μ=8.21 H_A: μ≠8.21

F H_0: μ=8.21 H_A: μ>8.21

c). Based on a random sample of 80 observations, a 95% confidence interval for the population proportion is (0.52, 0.74). Which of the following is true? Select all that apply. ( )

A The margin of error is 0.22.

B A larger confidence level would yield a wider confidence interval.

C The sample proportion is 0.63.

D A larger sample standard deviation would yield a narrower confidence interval. E We are 95% confident that the confidence interval will include every sample proportion.

d). In a t-test, the test statistic is 2.01. The investigator concludes that he should reject the null hypothesis. Which of the following scenarios does not justify the investigator’s decision? Select all that apply. ( )

A Sample size n = 10, α = 0.05, a one-sided “greater than” alternative test

B Sample size n = 10, α = 0.05, a two-sided test

C Sample size n = 20, α = 0.01, a one-sided “greater than” alternative test

D Sample size n = 20, α = 0.10, a two-sided test E Sample size n = 100, α = 0.05, a one-sided “greater than” alternative test

Answer 1

a) population proportions is denoted by P ̂.

b)

H₀: μ=8.

H_a: μ>8

c)

margin of error = (0.74 - 0.52)/2 = 0.11

proportion p = LCL + margin of error = 0.52+0.11 = 0.63

A larger confidence level would yield a wider confidence interval because increase in confidence increases the critical value.

A larger sample standard deviation would yield a narrower confidence interval which is not correct because standard deviation multiplies the critical value which increase the range of CI.

We are 95% confident that the confidence interval will include every sample proportion. Which is true because sample proportion is the middle value of the 95% CI.

the correct statements are B,C,E.

d)

B Sample size n = 10, α = 0.05, a two-sided test critical value = 2.262

C Sample size n = 20, α = 0.01, a one-sided “greater than” alternative test , critical value = 2.54