# A Solution to Assignment Conduct a Hypothesis Testing of Proportion Using Excel and Descriptive Statistics

## Assignment Instructions

1. Use descriptive statistics to summarize the proportion experiencing headache (grouped by the history of previous concussion and total), the proportion experiencing any symptoms (grouped by the history of previous concussion and total), and the mean number of symptoms experienced (grouped by sex and total). Discuss any relevant findings.

2. Develop 95% confidence intervals for (a) the proportion of all student-athletes experiencing headaches, and (b) the mean number of symptoms experienced by student-athletes participating in cheerleading. Comment on whether the appropriate assumptions are met for these methods.

3. Conduct a hypothesis test at an α = 0.05 significance level to determine if there is a difference in the mean number of symptoms experienced between male student-athletes and the mean number of symptoms experienced by female student-athletes. Include your hypotheses, test statistic, P-value, and conclusion. Comment on whether the appropriate assumptions are met for this test.

4. Conduct a hypothesis test at an α = 0.05 significance level to determine if the proportion of student-athletes experiencing headaches is different from the proportion indicated in the research. Include your hypotheses, test statistic, P-value, and conclusion. Comment on whether the appropriate assumptions are met for this test.

5. Given your results from the previous questions, what recommendations would you make to the state high school athletic association?

## Assignment Solutions

Below are questions that would help provide insight into the findings of this research. Please answer each of these and provide interpretations of the results.

1. Use descriptive statistics to summarize the proportion experiencing headache (grouped by the history of previous concussion and total), the proportion experiencing any symptoms (grouped by the history of previous concussion and total), and the mean number of symptoms experienced (grouped by sex and total). Discuss any relevant findings.

 Concussion History Yes NO NO 33 15 Yes 76 30

 Concussion History Yes No No 0.6875 0.3125 Yes 0.716981 0.283019

Of those who have experienced concussion before, 71.698% of those have had headaches, compared to 68.75% of those who haven’t experienced concussion before.

 Number of Symptoms Female Male Mean 6 Variance 34.85714286 11.01807018 Observation 78 76

The average number of symptoms experienced by male student-athletes is 2.40789 compared to 6 for female student-athletes.

2. Develop 95% confidence intervals for (a) the proportion of all student-athletes experiencing headaches, and (b) the mean number of symptoms experienced by student-athletes participating in cheerleading. Comment on whether the appropriate assumptions are met for these methods.

(a)

The 95% confidence interval for the proportion of all student-athletes experiencing headaches is (0.22038, 0.364036)

(b)

The 95% confidence interval the mean number of symptoms experienced by student-athletes participating in cheerleading is (4.815597, 10.44756).

3. Conduct a hypothesis test at an α = 0.05 significance level to determine if there is a difference in the mean number of symptoms experienced between male student-athletes and the mean number of symptoms experienced by female student-athletes. Include your hypotheses, test statistic, P-value, and conclusion. Comment on whether the appropriate assumptions are met for this test.

Null hypothesis: Average number of symptoms experienced between male student-athletes and the mean number of symptoms experienced by female student-athletes are equal

Alternate hypothesis: Average number of symptoms experienced between male student-athletes and the mean number of symptoms experienced by female student-athletes aren’t equal

T-test: Two-Sample Assuming Equal Variances

 Female Male Mean 6 2.407894737 Varience 34.85714286 11.01807018 Observations 78 76 Pooled Variance 23.09444252 Hypothesized Mean Difference 0 df 152 T-test 4.637554754 P(T,=t) one-tail 3.77241E-06 t Critical one tail 1.654940175 t Critical one tail 1.654940175 t Critical one tail 1.654940175

The test statistic is equal to 4.6375, df = 152, p-value = 7.5448*10-6< 0.05. Therefore, at 0.05 significance level, we reject the null hypothesis and conclude that the average number of symptoms experienced between male student-athletes and the mean number of symptoms experienced by female student-athletes aren’t equal

4. Conduct a hypothesis test at an α = 0.05 significance level to determine if the proportion of student-athletes experiencing headaches is different from the proportion indicated in the research. Include your hypotheses, test statistic, P-value, and conclusion. Comment on whether the appropriate assumptions are met for this test.

The research suggests that the proportion of student-athletes experiencing headaches would be close to 30.5%.

Null hypothesis: the proportion of all student-athletes experiencing headaches is 30.5%

Alternate hypothesis: the proportion of all student-athletes experiencing headaches isn’t 30.5%

We will use the one-sample Z-test to test the hypothesis.

 Headache Yes 45 Total 154 Proportion 0.292208 95%  Confidence Interval Lower Upper 0.364036 Hypothesized Proportion 0.305 Z-Statistics -0.3448 P-Value 0.730247

The value of the Z-statistic is -0.3448, p-value = 0.73 > 0.05. Therefore, at a 0.05 significance level, we fail to reject the null hypothesis and conclude that the proportion of all student-athletes experiencing headaches is 30.5%

5. Given your results from the previous questions, what recommendations would you make to the state high school athletic association?

Better rules for concussion guidelines, so that those with previous concussions have recovered well enough to participate further in the competitions.