Question

Test the claim about the population mean μ at the level of significance α. Claim: μ ≠ 0; α = 0.05; σ = 2.62 Sample statistics: = -0.69, n = 60 Fail to reject H0. There is enough evidence at the 5% level of significance to support the claim. Reject H0. There is enough evidence at the 5% level of significance to reject the claim. Reject H0. There is enough evidence at the 5% level of significance to support the claim.

Answer 1

Correct option:

Fail to reject H₀. There is enough evidence at the 5% level of significance to support the claim.

Explanation:

The claim to be tested is:

Claim: μ ≠ 0.

The information provided is:

α = 0.05

σ = 2.62

Sample statistics: = -0.69

n = 60

As the population standard deviation is provided, it can be determined that a z-test for single is used to performed the test.

Decision rule:

If the p-value of the test is less than the significance level, α then the null hypothesis will be rejected and vice-versa.

Compute the p-value as follows:

`p-value=2P(Z<-0.69)\\=2* [1-P(Z<0.69)]\\=2* [1-0.7549]\\=0.4902`

*Use a z-table for the probability.

The p-value = 0.4902 > α = 0.05.

The null hypothesis was failed to rejected at 5% level of significance.Thus, it can be concluded that there is enough evidence at the 5% level of significance to support the claim.