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
Step-by-step 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
