Question

A hypothetical investigation on rider satisfaction with a particular public transit system serving commuting residents of British California (BC) and Prince Edward’s County (PEC) offers some interesting findings. The proportion of commuters from BC that indicated low satisfaction with the transit system’s service in the 2018 calendar year was 65 percent, and the proportion from PEC was 70 percent. These point estimates were based on samples of 5,380 BC commuters and 6,810 PEC commuters, whose system-using commuters number in the millions.

(i)

In order to compute a valid confidence interval, what values/conditions must be satisfied?

(ii)

Assume that we may validly construct confidence intervals, and proceed with computing a 95% confidence interval for the difference between the proportions of British Californian commuters and Prince Edward County commuters who report low satisfaction with the public transit system.

-Background information for this question

Q:

Here, conduct a hypothesis test to ascertain whether the data given in Problem 2 offer strong evidence that the proportion of commuters from British California expressing low satisfaction with the transit system differs from the Prince Edward County proportion.  

To do this problem correctly, make sure you consult Section 6.2.3, pages 219-221, in OpenIntro Statistics, 4th Edition.

(i)

In order to conduct the hypothesis test, what values/conditions must be satisfied?

(ii)

How do we express the null and alternative hypotheses?

(iii)

Go ahead with the test. What is the value on your test statistic?

(iv)

What is the conclusion of your test?

Among the answer choices that follow, CHOOSE THE BEST COMBINATIONS OF THE OPTIONS GIVEN IN (i) AND (ii) AND (iii) AND (iv).

Group of answer choices

a.

(i)

The product of 5,380 and 68 percent must equal or surpass 10, as must the product of 5,380 and 0.32; samples from BC and PEC must be selected independently; the sizes of the samples of system-using commuters must fall below 10 percent of the population sizes; and samples selection must be randomized.

(ii)

H_0:   p_BC = p_PEC

H_A: p_BC < p_PEC

(iii)

-5.68

(iv)

We conclude that the proportion of commuters from BC giving low satisfaction ratings to the transit system is less than the proportion of PEC commuters giving low satisfaction ratings.

b.

(i)

The product of 5,380 and 68 percent must equal or surpass 10, as must the product of 5,380 and 0.32; samples from BC and PEC must be selected independently; the sizes of the samples of system-using commuters must fall below 10 percent of the population sizes; and samples selection must be randomized.

(ii)

H_0:   p_BC = p_PEC

H_A: p_BC ≠ p_PEC

(iii)

-5.87

(iv)

We conclude that the proportion of commuters from BC giving low satisfaction ratings to the transit system differs from the proportion of PEC commuters giving low satisfaction ratings.

c.

(i)

The product of 6,810 and 68 percent must equal or surpass 10, as must the product of 6,810 and 0.32; samples from BC and PEC must be selected independently; the sizes of the samples of system-using commuters must fall below 10 percent of the population sizes; and samples selection must be randomized.

(ii)

H_0:   p_BC = p_PEC

H_A: p_BC ≠ p_PEC

(iii)

-5.78

(iv)

We conclude that the proportion of commuters from BC giving low satisfaction ratings to the transit system differs from the proportion of PEC commuters giving low satisfaction ratings.

d.

(i)

The product of 6,810 and 68 percent must equal or surpass 10, as must the product of 6,810 and 0.32; samples from BC and PEC must be selected independently; the sizes of the samples of system-using commuters must fall below 10 percent of the population sizes; and samples selection must be randomized.

(ii)

H_0:   p_BC = p_PEC

H_A: p_BC   < p_PEC

(iii)

-5.68

(iv)

We conclude that the proportion of commuters from BC giving low satisfaction ratings to the transit system is less than the proportion of PEC commuters giving low satisfaction ratings.

e. None of the above answers sets is correct.

Answer 1

CondiHon ave randomy selectes are indepondan Both samples Both Camples ach 8am pler fncludes at least 10 Accesse & 10 fauluires hiPi10 1 Aample Aire Auffident lage iven Hhat nI3380 PI=O.65 D2= 6810 Pe-0.70 967- Conidence iorerval is from 2 table, y-0.07 -196 /(0.65-07) 196 0.65x0 507X0 3 6380 6810 (-0.051.96 4.23X10-+ (808X10- (0.05 t 0.0168) 0.0668 0.0332) 0.0668 (Pr-P 00332