Question

Suppose that in a random selection of 100 colored​ candies, 26​% of them are blue. The candy company claims that the percentage of blue candies is equal to 27​%. Use a 0.01 significance level to test that claim.

Identify the null and alternative hypotheses for this test. Choose the correct answer below.

A.

H0​: p=0.27

H1​: p<0.27

B.

H0​: p=0.27

H1​: p >0.27

C.

H0​: p≠0.27

H1​:p=0.27

D.

H0​: p=0.27

H1​:p ≠0.27

1) Identify the test statistic for this hypothesis test. (Round to two decimal places as​ needed.)

2) Identify the​ P-value for this hypothesis test. (Round to three decimal places as needed)

Identify the conclusion for this hypothesis test.

A.Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 27​%

B.Fail to reject H0.There is not sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 27​%

C. Reject H0. There is not sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 27​%

D.Reject H0.There is sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 27​%

Answer 1

The statistical software output for this problem is:

One sample proportion summary hypothesis test: p : Proportion of successes Ho p 0.27 Ha : p # 0.27 Hypothesis test results Proportion Count Total Sample Prop.Std. Err.Z-Stat P-value 0.26 0.044395946 -0.22524579 0.8218 26 100

Hence,

Hypotheses: Option D is correct.

Test statistic = -0.23

P-value = 0.822

Conclusion: Fail to reject H0.There is not sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 27​%. Option B is correct.