Question

This Question: 1 pt 15 of 20 (10 complete) Consider the hypotheses below Ho μ:50 H1 μ#50 Given that x-56. S-20. n-16, and -0.05, answer the questions below. a. What conclusion should be drawn? b. Use technology to determine the p-value for this test. a. Determine the critical value(s) The critical value(s) is(are) (Round to three decimal places as needed. Use a comma to separate answers as needed.) Determine the test statistic, t (Round to two decimal places as needed.) What conclusion should be drawn? Choose the correct answer below Reject the null hypothesis. The data do not provide sufficient evidence to conclude that the mean differs from μ B. A. 50 Reject the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from μ-50 C. Do not reject the null hypothesis The data provide sufficient evidence to conclude that the mean differs from μ-50 D. Do not reject the null hypothesis. The data do not provide sufficient evidence to conclude that the mean differs from u 50. b. Use technology to determine the p-value for this test. What is the p-value? p-value Round to three decimal places as needed.)

Answer 1

Part a

We are given

α = 0.05

n = 16

df = n – 1 = 16 – 1 = 15

So,

Critical values are -2.131, 2.131.

(by using t-table)

Test statistic formula is given as below:

t_xbar = (Xbar - µ)/[S/sqrt(n)]

We are given Xbar = 56, S = 20, n = 16, µ = 50

t_xbar = (56 – 50) / [ 20/sqrt(16)]

t_xbar = (56 – 50) / [ 20/4]

t_xbar = (56 – 50) / 5

t_xbar = 6/5

t_xbar = 1.20

Absolute value of t_xbar = 1.20 is less than absolute critical value 2.131

So, we do not reject the null hypothesis

Correct Answer: D.

Do not reject the null hypothesis. The data do not provide sufficient evidence to conclude that the mean differs from µ = 50.

Part b

P-value = 0.249

(by using excel)