Question

"Suppose we are testing the null hypothesis H0: = 20 and the alternative Ha: 20, for a Normal population with = 5. A random sample of 25 observations is drawn from the population, and we find that the sample mean of these observations is = 17.6. The P-value is closest to:"

Answer 1

Complete question is;

Suppose we are testing the null hypothesis H0: μ = 20 and the alternative Ha: μ ≠ 20, for a normal population with σ = 5. A random sample of 25 observations are drawn from the population, and we find the sample mean of these observations is x¯ = 17.6. The P-value is closest to:

a. 0.0668.

b. 0.0082.

c. 0.0164.

d. 0.1336

Answer:

Option D

Explanation:

We are given;

Null hypothesis; H0: μ = 20

Alternative hypothesis; Ha: μ ≠ 20

Population Standard deviation; σ = 5

Sample size; n = 25

Sample mean; x¯ = 17.6

Let's find the z-score from the formula;

z = (x¯ - μ)/(σ/√n)

z = (17.6 - 20)/(5/√5)

z = - 1.073

From online p-value from z-score calculator attached, using z = -1.073; two tailed hypothesis; significance value of 0.05,we have;

The P-Value is 0.283271.

Looking at the given options, the closest to the p-value is option D