Question

Use a​ t-test to test the claim about the population mean μ at the given level of significance alphaα using the given sample statistics. Assume the population is normally distributed.

​Claim: μ= 51,800; alphaα= 0.05 

Sample​ statistics:

x overbar= 50,889​, s=2800​, n=18

What are the null and alternative​ hypotheses? Choose the correct answer below.

A.

H0​: μ= 51,800

Ha​: μ≠ 51,800

B.

H0​:μ≤ 51,800

Ha​: μ> 51,800

C.

H0​: μ ≥ 51,800

Ha​: μ < 51,800

D.

H0​: μ ≠ 51,800

Ha​: μ = 51,800

What is the value of the standardized test​ statistic?

The standardized test statistic is? ___ (round to two decimal places)

What​ is(are) the critical​ value(s)?

The critical​ value(s) is(are) _____ (round to three decimal places as needed.)

Decide whether to reject or fail to reject the null hypothesis.

A.

Fail to rejectFail to reject H0. There is not enough evidence to reject the claim.

B.

Reject H0. There is not enough evidence to reject the claim.

C.

Reject H0.

There is enough evidence to reject the claim.

D.

Fail to reject H0. There is enough evidence to reject the claim.

Answer 1

SOLUTION:

From given data,

Use a​ t-test to test the claim about the population mean μ at the given level of significance alphaα using the given sample statistics. Assume the population is normally distributed.

​Claim: μ= 51,800; alphaα= 0.05 Sample​ statistics: x overbar= 50,889​, s=2800​, n=18

Where,

μ= 51,800

α= 0.05

= 50,889​,

s=2800​,

n=18

What are the null and alternative​ hypotheses? Choose the correct answer below.

H₀​: μ ≠ 51,800 (null hypotheses)

H_a​: μ = 51,800   (alternative hypotheses)

Answer : Option (D) is correct

What is the value of the standardized test​ statistic?

test​ statistic = ( - μ)/(s / sqrt(n))

test​ statistic = (50889 - 51800)/(2800 / sqrt(18))

test​ statistic = -1.38

The standardized test statistic is -1.38  (round to two decimal places)

What​ is(are) the critical​ value(s)?

We have α= 0.05  

Degree of freedom = n-1 = 18-1 = 17

Critical value = t_α,df = t_0.05,17 = 2.109

The critical​ value(s) is(are) 2.109 (round to three decimal places as needed.)

Decide whether to reject or fail to reject the null hypothesis.

Where,

test​ statistic = -1.38 < t_0.05,17 = 2.109 So,

Fail to reject Fail to reject H₀. There is not enough evidence to reject the claim.

Answer:option(A) is correct