Question

In: Statistics and Probability

15. A candy company makes five different colors of candies. Find the sample proportion of candies...

15. A candy company makes five different colors of candies. Find the sample proportion of candies that are green. Use that result to test the claim that 15​% of the​ company's candies are green. Use the data in the table​ below, the​ P-value method, and a significance level of 0.025.

What are the null and alternative​ hypotheses?

A. H 0 : p ≠ 0.15

H 1 : p = 0.15

B.H 0 : p > 0.15

H 1 : p = 0.15

C. H 0 : p = 0.15

H 1 : p > 0.15

D. H 0 : p = 0.15

H 1 : p ≠ 0.15

E.H 0 : p = 0.15

H 1 : p < 0.15

F.H 0 : p < 0.15

H 1 : p = 0.15

What is the test​ statistic?

Z=

​(Round to two decimal places as​ needed.)

What is the​ P-value?

​P-value=

​(Round to three decimal places as​ needed.)

What is the conclusion on the null​ hypothesis?

A.Reject the null hypothesis because the​ P-value is less than or equal to the significance​ level, a.

B.Reject the null hypothesis because the​ P-value is greater than the significance​ level, a.

C.Fail to reject the null hypothesis because the​ P-value is less than or equal to the significance​ level, a.

D.Fail to reject the null hypothesis because the​ P-value is greater than the significance​ level, a.

What is the final​ conclusion?

A.There is sufficient evidence to warrant rejection of the claim that 17 % of the​ company's candies are green.

B.There is not sufficient evidence to support the claim that 17 % of the​ company's candies are green.

C.There is not sufficient evidence to warrant rejection of the claim that 17 % of the​ company's candies are green.

D.There is sufficient evidence to support the claim that 17 % of the​ company's candies are green.

Solutions

Expert Solution

15)

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.15

Ha : p 0.15

n = 5

x = 1

= x / n = 1 / 5 = 0.2

P0 = 0.15

1 - P0 = 1 - 0.15 = 0.85

z = - P0 / [P0 * (1 - P0 ) / n]

= 0.2 - 0.15 / [(0.15 * 0.85) / 5]

= 0.313

Test statistic = 0.31

This is the right tailed test .

P(z > 0.31) = 1 - P(z < 0.31) = 0.3783

P-value = 2 * 0.3783 = 0.7566

= 0.025

P-value <

D.Fail to reject the null hypothesis because the​ P-value is greater than the significance​ level .

C.There is not sufficient evidence to warrant rejection of the claim that 17 % of the​ company's candies are green.


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