Question

Based on the information provided for this hypothesis testing, what decision should you come to? (Assume that the population is normally distributed). Note that you need to complete the 5 step hypothesis testing. Be sure to include the cut-off sample score, the sample score on the comparison distribution, and the conclusion you reach.

Mean=5, SD=1, Sample Score=7, .05 level of significance, one-tailed.

Answer 1

The hypothesis being tested is:

H₀: µ = 5

H_a: µ > 5

The test statistic, z = (x - µ)/σ

z = (7 - 5)/1

z = 2

The p-value for z = 2 is 0.9773.

Since the p-value (0.9773) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that the mean is greater than 5.

Or

The hypothesis being tested is:

H₀: µ = 5

H_a: µ < 5

The test statistic, z = (x - µ)/σ

z = (7 - 5)/1

z = 2

The p-value for z = 2 is 0.0228.

Since the p-value (0.0228) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the mean is smaller than 5.