Question

Dr. Smith was interested in examining if weekly exercise would produce a change in the stress levels among individuals in the population. In general population of college students, scores on a standardized stress test that are normally distributed with the mean µ = 20 and standard deviation σ = 5. Because it was not feasible to ask everyone in the population to exercise weekly, a sample of n = 16 individuals was selected, and the exercise training program was given to this sample. After exercising, the average stress score for this sample was ?̅ = 17. Can the researcher conclude that exercise would have an effect on stress levels? Round up to two decimal places. Use a two-tailed test and α = .05.

Q1: State your null hypothesis and research hypothesis in complete sentences.

Q2: what are the cut-off points?

Q3: What is the standard error?

Q4: What is the z-score?

Q5: Write your conclusion thoroughly.

Answer 1

1)

H0: = 20 ,

Ha: 20

2)

z critical values at 0.05 significance level = -1.96 , 1.96

3)

Standard error = / sqrt ( n) = 5 / sqrt(16) = 1.25

4)

z-score = ( - ) / SE

= ( 17 - 20) / 1.25

= -2.4

5)

Since test statistics > 1.96 reject H0.

We have sufficient evidence to conclude that exercise would have an effect on stress levels.