Accepting null/alternate hypnothesis at various significance levels

[KLan]

Homework Statement

Given that a 95% confidence interval (or 0.05 significance level, α=0.05) for population proportion p is (0.11, 0.17), which statement is true regarding the hypotheses:
(null hypothesis) H0: p = 0.15
(alternate hypothesis) H1: p ≠ 0.15

a) Reject H0 at α = 0.05
b) Reject H0 at α = 0.10
c) Accept H0 at α = 0.05
d) Accept H0 at α = 0.10

Homework Equations

The Attempt at a Solution

Since it's a two-sided test, each side will have α = 0.025 at the 95% significance level. But p = 0.15 is within both α = 0.05 and α = 0.10 isn't it? So wouldn't H0 be accepted at both 0.05 and 0.10?
Kind of lost here. =/

 

[mighty2000]

Based on the information provided, the correct answer would be c) Accept H0 at α = 0.05. This is because the 95% confidence interval for the population proportion falls within the range of the null hypothesis (p = 0.15). This means that there is no significant difference between the observed proportion and the expected proportion of 0.15. Additionally, since the confidence interval does not include the null hypothesis value, we cannot reject the null hypothesis at the 0.05 significance level.

It is important to note that the significance level, α, is the probability of rejecting the null hypothesis when it is actually true. In this case, α = 0.05 means that there is a 5% chance of rejecting the null hypothesis when it is actually true. Therefore, if the observed proportion falls within the confidence interval, we cannot reject the null hypothesis at this significance level.

I hope this helps clarify your understanding. If you have any further questions, please feel free to ask. Keep up the good work in your studies!