Question

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Consider the following hypothesis test.

H₀: μ ≥ 50

H_a: μ < 50

A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use

α = 0.01.

(a)

x = 49 and s = 5.2

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.

Reject H₀. There is sufficient evidence to conclude that μ < 50.

Do not reject H₀. There is insufficient evidence to conclude that μ < 50.    

Reject H₀. There is insufficient evidence to conclude that μ < 50.

Do not reject H₀. There is sufficient evidence to conclude that μ < 50.

(b)

x = 48 and s = 4.5

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.

Reject H₀. There is sufficient evidence to conclude that μ < 50.

Do not reject H₀. There is insufficient evidence to conclude that μ < 50.    

Reject H₀. There is insufficient evidence to conclude that μ < 50.

Do not reject H₀. There is sufficient evidence to conclude that μ < 50.

(c)

x = 51 and s = 6.0

Find the value of the test statistic.

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

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ < 50.

Do not reject H₀. There is insufficient evidence to conclude that μ < 50.    

Reject H₀. There is insufficient evidence to conclude that μ < 50.

Do not reject H₀. There is sufficient evidence to conclude that μ < 50.

Answer 1

a)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (49 - 50)/(5.2/sqrt(36))
t = -1.154

P-value Approach
P-value = 0.1282
As P-value >= 0.01, fail to reject null hypothesis.
Do not reject H0. There is insufficient evidence to conclude that μ < 50.

b)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (48 - 50)/(4.5/sqrt(36))
t = -2.667

P-value Approach
P-value = 0.0058
As P-value < 0.01, reject the null hypothesis.
Reject H0. There is sufficient evidence to conclude that μ < 50.

c)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (51 - 50)/(6/sqrt(36))
t = 1

P-value Approach
P-value = 0.8379
As P-value >= 0.01, fail to reject null hypothesis.

Do not reject H0. There is insufficient evidence to conclude that μ < 50.