Question

 

Consider the following hypothesis test. H0: μ = 100 Ha: μ ≠ 100 A sample of 65 is used. Identify the p-value and state your conclusion for each of the following sample results. Use α = 0.05. (a) x = 104 and s = 11.5 Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

State your conclusion.

Do not reject H0. There is sufficient evidence to conclude that μ ≠ 100.

Do not reject H0. There is insufficient evidence to conclude that μ ≠ 100.

Reject H0. There is sufficient evidence to conclude that μ ≠ 100.

Reject H0. There is insufficient evidence to conclude that μ ≠ 100.

(b) x = 96.5 and s = 11.0 Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.) p-value =

State your conclusion.

Do not reject H0. There is sufficient evidence to conclude that μ ≠ 100.

Do not reject H0. There is insufficient evidence to conclude that μ ≠ 100.

Reject H0. There is sufficient evidence to conclude that μ ≠ 100.

Reject H0. There is insufficient evidence to conclude that μ ≠ 100.

(c) x = 102 and s = 10.5 Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.) p-value =

State your conclusion.

Do not reject H0. There is sufficient evidence to conclude that μ ≠ 100.

Do not reject H0. There is insufficient evidence to conclude that μ ≠ 100.

Reject H0. There is sufficient evidence to conclude that μ ≠ 100.

Reject H0. There is insufficient evidence to conclude that μ ≠ 100.

Answer 1

a)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (104 - 100)/(11.5/sqrt(65))
t = 2.804

P-value Approach
P-value = 0.0067
As P-value < 0.05, reject the null hypothesis.
Reject H0. There is sufficient evidence to conclude that μ ≠ 100.

b)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (96.5 - 100)/(11/sqrt(65))
t = -2.565

P-value Approach
P-value = 0.0127
As P-value < 0.05, reject the null hypothesis.

Reject H0. There is sufficient evidence to conclude that μ ≠ 100

c)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (102 - 100)/(10.5/sqrt(65))
t = 1.536

P-value Approach
P-value = 0.1295
As P-value >= 0.05, fail to reject null hypothesis.

Do not reject H0. There is insufficient evidence to conclude that μ ≠ 100.