Question

a. Determine the appropriate critical​ value(s) for the test Upper H Subscript Upper A​: mugreater than12​, nequals11​, sigmaequals10.3​, alpha equals 0.05 .

Answer 1

Critical z-value = 1.64

Explanation:

We are given the following in the question:

Population mean, μ = 12

Sample size, n = 11

Alpha, α = 0.05

Population standard deviation, σ = 10.3

First, we design the null and the alternate hypothesis

`H_(0): \mu \leq 12\\H_A: \mu > 12`

Since population standard deviation is given, we use one-tailed z test to perform this hypothesis.

Now,
`z_(critical) \text{ at 0.05 level of significance } = 1.64`

Thus, the appropriate critical values is 1.64.

If the calculated z-statistic is greater than the critical value, we fail to accept the null hypothesis and reject it.

If the calculated z-statistic is less than the critical value, we fail to reject the null hypothesis and accept it.