Question

7. Elliot has finally figured out that his veggie tacos had WAY too much cilantro. He finds a new recipe and invites 500 loyal customers to come and try it. 394 customers indicate that they like the new veggie taco better than the old recipe. Elliot wants to know if 75% of the population will prefer the new recipe and YOU are the savvy business statistician he's found to figure it out! May the odds be ever in your... flavor. Set up the null and the alternative hypotheses. b. Determine the test statistic. Determine the p-value. d. At 95% confidence, test to determine if more than 80% of the population will prefer the new recipe. a. C.

PLEASE SHOW WORK FOR EACH ANSWER

Answer 1

Here we have: n=500 x=394 Sample proportion: Ộ = 394 = 0.788 500 = n a = 1-0. Hypothesis: H: P=0.75 H: P = 0.75 Test statistics: z-test 0.788-0.75 = Z= = P-p p(1-p) = 1.96 0.75(1-0.75) 500 n

Critical value: Zcrit= za 2 = 20.05/2 = +1.96 P-value = 2p (Z >|1.961) = 0.049996 Reject the null hypothesis. Conclusion: Here we have sufficient evidence to reject the null hypothesis. z-observed value is greater than z-critical value. And p-value is less than alpha vlaue Confidence interval: (1-6) P= P +z* n = = 0.788 + 1.96 * 10.788(1-0.788) 500 = 0.788 + 0.036

= 0.752 <P<0.824 Here we are 95% confident that the population proportion 0.752 to 0.824, we can see that this confidence interval also include more than 80% values