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A restaurant owner believes diners at her restaurant are more likely to order a vegetarian entree...

A restaurant owner believes diners at her restaurant are more likely to order a vegetarian entree while eating on a weekday than on the weekend. If this is true, she plans to offer a daily vegetarian special during the week. She collects a random sample of 87 diners eating in the restaurant on Monday, Tuesday, Wednesday, Thursday, or Friday and a random sample of 68 diners eating in the restaurant on Saturday or Sunday. She finds the 19% of weekday diners and 16% of weekend diners order a vegetarian option. Test her hypothesis.


(a) State the null and alternative hypotheses using correct notation.


(b) What type of test should you use? Explain how the conditions for this test are met.


(c) Choose an appropriate level of significance, and explain why you chose this value.


(d) Calculate the test statistic to two decimal places and the p-value to four decimal places.


(e) What is the result of the hypothesis test? Do you reject or fail to reject the claim?


(f) What are your conclusions. Should the restaurant owner offer the new vegetarian special?

math   Statistics-And-Probability   
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Answer #1

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(b)

z test for comparing proportions

Yes conditions are met because samples are large.

(c)

The appropriate level of significance is 0.05.

(f)

We cannot conclude that diners at her restaurant are more likely to order a vegetarian entree while eating on a weekday than on the weekend. The restaurant owner should not offer the new vegetarian special.

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