# 15. A candy company makes five

15. A candy company makes five different colors of candies. Findthe sample proportion of candies that are green. Use that result totest the claim that 15% of the company’s candies are green. Usethe data in the table below, the P-value method, and asignificance 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 thanor equal to the significance level, a.

B.Reject the null hypothesis because the P-value is greaterthan the significance level, a.

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

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

What is the final conclusion?

A.There is sufficient evidence to warrant rejection of the claimthat 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 theclaim that 17 % of the company’s candies are green.

D.There is sufficient evidence to support the claim that 17 % ofthe company’s candies are green.

Answer:

15)

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H_{0} : p = 0.15

H_{a} : p 0.15

n = 5

x = 1

= x / n = 1 / 5 = 0.2

P_{0} = 0.15

1 – P_{0} = 1 – 0.15 = 0.85

z = – P_{0} / [P_{0*} (1 – P_{0} ) / 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 isgreater than the significance level .

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