Answer:
Option c: Fail to reject the null hypothesis at α = 0.10
Step-by-step explanation:
We are given;
Population mean; μ = 70
population standard deviation; σ = 17.32
Sample mean; x¯ = 72.43
Sample size; n = 35
Thus;
Null hypothesis; H0: μ = 70
Alternative hypothesis; Ha: μ > 70
Z-score formula is;
z = (x¯ - μ)/(σ/√n)
z = (72.43 - 70)/(17.32/√35)
z = 2.43/2.9276
z = 0.83
From online p-value from z-score calculator attached, using z = 0.83; significance level = 0.05 and one tailed hypothesis, we have;
P-value ≈ 0.2033
It's more than the significance value, so we will fail to reject the null hypothesis at α = 0.05
Similarly, From online p-value from z-score calculator attached, using z = 0.83; significance level = 0.01 and one tailed hypothesis, we have;
P-value ≈ 0.2033
It's more than the significance value, so we will fail to reject the null hypothesis at α = 0.01
Similarly, From online p-value from z-score calculator attached, using z = 0.83; significance level = 0.10 and one tailed hypothesis, we have;
P-value ≈ 0.2033
It's more than the significance value, so we will fail to reject the null hypothesis at α = 0.10
From the 3 significance values, the correct option is option c. fail to reject the null hypothesis at α = 0.10
