Question

Field tests of a​ low-calorie sport drink found that 86 of the 110 who tested the beverage preferred it to the regular​ high-calorie drink. A​ break-even analysis indicates that the launch of this product will be profitable if the beverage is preferred by 74​%of all customers. Complete parts a through c.​

(a) State the null and alternative hypotheses. Let p be the proportion of customers who prefer the new​ low-calorie drink. Choose the correct answer below. (SOLVED)

A. H0​: p≤ 0.78​; Ha​:p> 0.78

B. H0​: p ≤ 0.74​; Ha​: p > 0.74 Your answer is correct.

C.H0​: p ≥ 0.74​; Ha​: p < 0.74

D.H0​:p ≥ 0.78 Ha​: p < 0.78

​(b) Describe Type I and Type II errors in this context. Choose the correct answer below. (SOLVED)

A.Launching the new​ low-calorie drink unnecessarily is a Type I error. Missing the opportunity to launch the new​ low-calorie drink is a Type II error. Your answer is correct.

B.Missing the opportunity to launch the new​ low-calorie drink is a Type I error. Launching the new​ low-calorie drink unnecessarily is a Type II error.

C.Launching the new​ low-calorie drink is a Type I error. Missing the opportunity to launch the new​ low-calorie drink is a Type II error.

D.Launching the new​ low-calorie drink unnecessarily is a Type I error. Taking the opportunity to launch the new​ low-calorie drink is a Type II error.

​(c) Find the​ p-value for a test of the null hypothesis. (PLEASE SOLVE)

​p-value= ________​(Type an integer or decimal rounded to three decimal places as​ needed.)

Answer 1

given information 2386 ne 110 , p = 862 078 No Null hypothous! P5074 . Alternative hypotharis p.70.74 test Statistic 22 Ø-P . PLi-P a 0.782 -0.74 0-74x11-0:74) € 1.004 CV' ni 110 P-value = P(271.009) = 1- P12< 1.004)= 1 0842 01577 PIZ< 1.004)0.8423 (using Exceda Noerys.oist (1.004, TRUE [p-value = 0.158 Answer