In: Statistics and Probability
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.
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.