Question

Use a​ t-test to test the claim about the population mean at the given level of significance using the given sample statistics. Assume the population is normally distributed. ​Claim: ​;     Sample​ statistics: ​, s​, n What are the null and alternative​ hypotheses? Choose the correct answer below. A. H0​: Ha​: B. H0​: Ha​: C. H0​: Ha​: D. H0​: Ha​: What is the value of the standardized test​ statistic? The standardized test statistic is nothing. ​(Round to two decimal places as​ needed.) What is the​ P-value of the test​ statistic? ​P-value nothing ​(Round to three decimal places as​ needed.)

Answer 1

Complete question is;

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

Claim: μ ≥ 8300,α= 0.10

Sample statistics: ¯x = 8000, s = 440, n = 24

a. What are the null and alternative hypotheses?

b. What is the value of the standardized test statistic? (Round to 2 decimal places as needed.)

c. What is the p-value? (Round to three decimal places as needed.)

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

Answer:

A) Null hypothesis:H0: μ ≥ 8300

Alternative Hypothesis:Ha:μ < 8300

B) t = -3.34

C) p-value = 0.001

D) we will reject the null hypothesis

Step-by-step explanation:

A) We are told that the claim is: μ ≥ 8300. Thus, the null hypothesis would be the claim. So;

Null hypothesis:H0: μ ≥ 8300

Also, alternative hypothesis would be;

Alternative Hypothesis:Ha:μ < 8300

B)Formula for standardized test statistic with a t-test is;

t = (¯x - μ)/√(s/n)

Plugging in the relevant values, we have;

t = (8000 - 8300)/√(440/24)

t = -3.34

C) From online p-value from t-score calculator attached using t = -3.34, n = 24, significance level = 0.01, DF = 24 - 1 = 23 and a one - tailed test, we have;

p-value = 0.001421 ≈ 0.001

D) The p-value of 0.001 is less than the significance value of 0.01,thus we will reject the null hypothesis