You wish to test the following claim ( H a ) at a significance level of α = 0.001 .

Question

You wish to test the following claim () at a significance level of .             You believe the population is normally distributed and you know the standard deviation is . You obtain a sample mean of  for a sample of size .What is the test statistic for this sample? (Report answer accurate to three decimal places.)  What is the p-value for this sample? (Report answer accurate to four decimal places.) .

Answer 1

Compute the Standard Error as σ_X-bar equal to σ_X/√n or 16.7/√48. Next, take the Z-Test Statistic given by

z = (x-bar − μ₀) ÷ σ_X-bar or (74.8 − 72.6) ÷ (16.7/√48).

The area under the Standard Normal Curve to the left of z = (74.8 − 72.6) ÷ (16.7/√48) or 0.9126974315 is given with high accuracy by a calculator program as (0.3192991524 + 0.5) or 0.8192991524.

Here the alternative hypothesis H_a is a "not-equal-to" hypothesis and the Z-Test Statistic is positive, so the

p-value is obtained by 2(1 − 0.8192991524) or 0.3614016952.

0.3614016952 is larger than the significance level of 0.001. Then the null hypothesis H₀ : μ = 72.6 cannot be rejected at the 0.001 significance level. That is, it cannot be said that the sample mean has any difference from the norm.

The Z-Test Statistic is equivalent to 0.913.

The P-Value is equivalent to 0.3614.