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# Hypothesis Testing: Z test for Population Proportion

The policy of the Suburban Transit Authority (STA) is to add a bus route if more than 45% of the potential commuters indicate they would use the particular route. A sample of 70 commuters revealed that 39 would use a proposed route from Bowman Park to the downtown area. Does the Bowman-to-downtown route meet the STA criterion? Use the .05 significance level.

A. What is the null hypothesis?
A. ¦Ì = 45%
B. ¦Ì ¡Ù 45%
C. ¦Ð = 45%
D. ¦Ð ¡Ý 45%
E. ¦Ð < 45%

B. What is the critical value?
A. ?.96
B. 1.96
C. -1.96
D. 1.65
E. Something else

C. What type of test is appropriate for this problem?
A. Z-test ?single samples
B. Z-test ?proportions
C. T-test of independence
D. Paired samples t-test
E. ANOVA

D. What is the test statistic?
A. .251
B. 1.66
C. 1.68
D. 1.96
E. .0926

E. What is the p-value?
A. .251
B. 1.66
C. 1.68
D. 1.96
E. .0926

F. What is the decision?
A. Accept the null of no difference. The Bowman-to-downtown route meets the STA criterion.
B. Reject the null of no difference. The Bowman-to-downtown route meets the STA criterion.
C. Accept the null of no difference. The Bowman-to-downtown route DOES NOT meet the STA criterion.
D. Reject the null of no difference. The Bowman-to-downtown route DOES NOT meet the STA criterion.

#### Solution Summary

The solution provides step by step method for the calculation of test statistic for population proportion. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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