Question

A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86]. At the 1% significance level, what decision should be made regarding the following hypothesis test with LaTeX: H_0H 0: LaTeX: \mu=0μ = 0 versus LaTeX: H_1H 1: LaTeX: \mu\\e0μ ≠ 0?

Answer 1

Decision rule: Do not reject
`H_o`; we cannot conclude that the mean differs from zero

Explanation:

From the given information:

The null hypothesis and alternative hypothesis is given as:

`H_o: \mu = 0 \\ \\ H_1 : \mu \\e 0`

And the 99% confidence interval for the population mean
`\mu` is: [−3.79, 5.86]

The significance level ∝ = 1 - 0.99 = 0.01

We will notice that the 99% confidence interval for the population mean
`\mu` contains the null hypothesis mean value which is equal to zero.

Thus, we do not reject the null hypothesis at the significance level ∝ = 0.01

∴

Decision rule: Do not reject
`H_o`; we cannot conclude that the mean differs from zero