Question

1. The Friendly Fitness Club recorded the weights of its members before they began their fitness program. They discovered that the weights were normally distributed with a mean of 85kg and a standard deviation of 9.5. After the fitness program was finished, the director of the club randomly selected 49 participants and recorded their weights. She found that the mean weight for this group was 82kg. Use a one-tailed test with an alpha level set at .05 to determine if the program was effective in reducing weight. Follow the 4-step hypothesis testing to answer the research question.

Step 1 (1pt): H₀:

                      H_A:

**Is this a one-tailed or two-tailed test? (1pt)

Step 2 - State the criterion for rejection (1pt):

Step 3 – Compute and report the test statistic (1pt):

Step 4 – Make a decision and report conclusion in proper format (1pt):

**Remember when hand calculating, you will compare your Z_obt to Z_crit.

2. Calculate the effect size (Cohen’s d) for the above problem, and provide a written interpretation. (2pts)
3. Calculate the 99% confidence intervals and explain what they indicate (1pt).

4. What, exactly, does a p-value tell you? (1pt)
5. Interpret a p-value of .03 (1pt)
6. What does it mean to say that a result is statistically significant at the .05 alpha level? (1pt)


Answer 1

H0: mu = 85
Ha: mu < 85

This is one tailed test, left tailed

z-critical = -1.645
If z-obt < z-critical, reject H0

Test statistic,
z = (82 - 85)/(9.5/sqrt(49))
z = -2.2105

p-value = 0.0135

Reject H0, this means that the progam is effective in reducing the weights

99% CI = (82 - 2.58*9.5/sqrt(49), 82 + 2.58*9.5/sqrt(49))
= (78.4986, 85.5014)