Question

Testing to see if there is evidence that the proportion of US citizens who can name the capital city of Canada is greater than 0.75. a. (3pts) State the Null and Alternative Hypotheses. Also, state the direction of the test Using the following possible sample results: • Sample A: 31 successes out of 40 • Sample B: 34 successes out of 40 • Sample C: 27 successes out of 40 • Sample D: 38 successes out of 40 b. State which of the possible sample results provides the most evidence against the null. Briefly explain (2pts) c. State which (if any) of the possible results provide no evidence for the alternative. Briefly explain (2pts)

Answer 1

b) B and D and c) A and C

Explanation:

The hypotheses would be:

`H_0: p =0.75\\H_a: p >0.75`

(Right tailed test at 5% level)

Sample proportions are

Sample A B C D

Success 31 34 27 38

Proportion p 0.775 0.85 0.675 0.95

Std error

(sqrtpq/n) 0.066 0.056 0.074 0.034

p diff

p-0.75 0.025 0.10 - 0.075 0.20

Z stat

p diff/SE 0.0757 1.77 1.01 5.80

p value 0.469 0.038 0.156 0.000001

we find that p value is more smaller than alpha, the more accurate the alternate hypothesis.

b) Only B and D provide against the null. Because p <0.05

c) A and C provide no evidence for the alternative because p >0.05