Question

h₁: μ ≠ 8.5 claim this hypothesis test is a two - tailed test. part: 1 / 5 part 2 of 5 find the critical value(s). round the answer to at least two decimal places. if there is more than one critical value, separate them with commas. critical value(s):

Explanation:

Step1: Identify Test Type

The hypothesis test is two - tailed ($H_1:\mu
eq8.5$), so we need critical values for both tails. We assume a common significance level, say $\alpha = 0.05$ (since it's not given, this is a standard assumption for such problems). For a two - tailed test with $\alpha=0.05$, we are dealing with a normal distribution (assuming z - test, or t - test, but if we assume z - test for large samples or when population standard deviation is known). For a z - test, the critical values are found by splitting $\alpha$ into two tails, so $\alpha/2=0.025$ in each tail.

Step2: Find Critical Z - Values

We look for the z - scores such that $P(Z < - z_{\alpha/2})=0.025$ and $P(Z>z_{\alpha/2}) = 0.025$. From the standard normal distribution table (or z - table), the z - score corresponding to a cumulative probability of $0.025$ (left - tail) is $z=- 1.96$ and the z - score corresponding to a cumulative probability of $1 - 0.025=0.975$ (right - tail) is $z = 1.96$. If we were using a t - test, we would need the degrees of freedom, but since it's not given, the most common case for a two - tailed test with no degrees of freedom specified (or when sample size is large) is the z - test with critical values $\pm1.96$.

Answer:

• 1.96, 1.96