Question

A sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level. Use the critical -value approach.

= 20.5, n = 11 , σ = 7, H0: μ = 18.7; Ha: μ ≠ 18.7, α = 0.01

Answer 1

Answer:

 Z = 0.8528 < 2.576

The calculated value Z = 0.8528 < 2.576 at 0.01 level of significance

Null hypothesis is Accepted at 0.01 level of significance.

There is no significance difference between the means

Step-by-step explanation:

Given data

size of the sample 'n' = 11

mean of the sample x⁻ =20.5

Mean of the Population μ = 18.7

Standard deviation of Population σ = 7

Test statistic

                  $Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }$

                  $Z = \frac{20.5 -18.7}{\frac{7}{\sqrt{11} } }$

                  $Z = \frac{1.8}{2.1105}$

                  Z = 0.8528

critical Value

$Z_{\frac{\alpha }{2} } = Z_{\frac{0.01}{2} } = Z_{0.005} = 2.576$

The calculated value Z = 0.8528 < 2.576 at 0.01 level of significance

Null hypothesis is Accepted at 0.01 level of significance.

There is no significance difference between the means

Answer 2

Answer:Answer:

B. 18.7 ± 9.7

Step-by-step explanation: