Question

Use the t-distribution and the sample results to complete the test of the hypotheses. Use a 5% significance level. Assume the results come from a random sample, and if the sample size is small, assume the underlying distribution is relatively normal.

Test H0: μ= 4 vs Ha: μ≠4 using the sample results x= 4.8, s= 2.3, with n= 15.

(a) Give the test statistic and the p-value.

Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.

test statistic = ___

p-value = ___

(b) What is the conclusion?

Reject or H0.

Answer 1

a. test statistic = 1.35

p-value = 0.198439

b. Support the null hypothesis.

Explanation:

Hello!

a.

So you have the hypothesis:

H₀:μ=4

H₁:μ≠4

with the sample information you calculate the statistic using the t-distribution with 14 (n-1) degrees of freedom:

t=x[bar] - μ ⇒ t= 4.8 - 4 = 0.8 = 1.347≅ 1.35

s/√n 2.3/√15 0.59

Reminder:

The p-value is defined as the probability corresponding to the calculated statistic (or of obtaining a value as extreme as the value of the statistic) if possible under the null hypothesis.

p-value: 0.198439

b.

Since the calculated p-value is greater than the significance level, you don't reject the null hypothesis.

I hope you have a SUPER day!