Question

You are a researcher that wants to test whether exercising for 20 mins per day affects happiness. You have a database for students with mean happiness of 65 and SD of 13. You know that the database is normally distributed and conduct an experiment which you have 5 students exercise 20mins/day for 7days. After the last day they rate their happiness on a scale of 1-100 with 1 being extremely unhappy and 100 indicating extremely happy. Their result as follows subject 1=98 happiness subject 2=82 3=84 4=85 5=91. Alpha=0.01.

1. What are your hypothesis

2. Describe characteristics of comparison distribution.

3. What is your cutoff critical z score

4. What is your sample zscore.

5. What is your decision regarding null hypothesis? Explain why you made these decisions.

Answer 1

(1)

H0: Null Hypothesis: = 65

HA: Alternative Hypothesis: 65

EXPLANATION: The research question is: Whether exercising for 20mins affects happiness and NOT increases happiness. So, it is a two tail test and NOT a right tail test with > 65.

(2)

The characeristics of comparison distribution are got as follows:

n = Sample Size = 5

= Sample Mean = 440/5 = 88

s = Sample SD = 6.5192

(3)

= 0.01

From Table, critical value of Z = 2.576

(4)
SE = /

= 13/ = 5.8137

Test statistic is:
Z = (88 - 65)/5.8137 = 3.9562

(5)

Since the calculated value of Z = 3.9562 is greater than critical value of Z= 2.576, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that exercising affects happiness.