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A 20-minute consumer survey that included a $5 Starbucks gift card was emailed to 500 adults aged 25-34. The survey resulted in 65 responses. The same 20-minute consumer survey was emailed to 500 adults aged 25-34 without the Starbucks gift card. The survey resulted in 45 responses. We would like to know if the inclusion of a Starbucks gift card led to any change in survey response rate. Which of the following hypotheses should be used?
A. Null Hypothesis: mul (average number of responses with Starbucks gift card)<= muo(average number of responses without Starbucks gift card) Alternative Hypothesis: mu1 ( average number of responses with Starbucks gift card)> muo(average number of responses without Starbucks gift card)
B. Null Hypothesis: mu1 (average number of responses with Starbucks gift card)= mud (average number of responses without Starbucks gift card) Alternative Hypothesis: mu1 ( average number of responses with Starbucks gift card) \= mul ( average number of responses without Starbucks gift card) * \= means "not equal to"
C. Null Hypothesis: pi1 (rate with Starbucks gift card)= pi2 (rate without Starbucks gift card) Alternative Hypothesis: pi1 (rate with Starbucks gift card) (= pi2 (rate without Starbucks gift card) * \= means "not equal to"
D. Null Hypothesis: pi1 (rate with Starbucks gift card) - pi2 (rate without Starbucks gift card)<=0 Alternative Hypothesis: pi1 (rate with Starbucks gift card) - pi2 (rate without Starbucks gift card) > 0

Answer :

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Answer:

D. Null Hypothesis: pi1 (rate with Starbucks gift card) - pi2 (rate without Starbucks gift card)<=0 Alternative Hypothesis: pi1 (rate with Starbucks gift card) - pi2 (rate without Starbucks gift card) > 0

Step-by-step explanation:

The test described above test the difference in proportion :

With Starbucks gift card :

x1 = 65 n1 = 500

Phat 1 = x1 / n1

Phat 1 = 65 /500 = 0.13

Phat1

Without Starbucks gift card :

x2 = 45 n2 = 500

Phat1 = x2 / n2

Phat 2 = 45 / 500 = 0.09

To test the difference in proportion :

Phat 1 > Phat 2 (alternative)

Null takes the stance that there is no difference in proportion

Phat1 - phat2 <=0

Alternative claims that there is difference on proportion such that phat 1 is greater than phat 2

Phat 1 - phat > 0

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