Final answer:
Performing a hypothesis test at the 0.10 level of significance, the test results suggest that there is not enough evidence to support the claim that the percent is larger for students who play intramural sports.
Step-by-step explanation:
To determine if the percent of students who play intramural sports and receive a degree within six years is larger than the overall percentage, we can perform a hypothesis test at the 0.10 level of significance.
First, we define the null hypothesis (H0) as the percent of students who play intramural sports receiving a degree within six years is the same as the overall percentage.
The alternative hypothesis (Ha) is that the percent is larger for students who play intramural sports.
We can calculate the test statistic using the formula: z = (p - P) / sqrt((P * (1-P)) / n), (where p is the proportion of students who played intramural sports and received a degree, P is the overall percentage of students receiving a degree, and n is the total number of students who played intramural sports).
For the given data, p = 453/800 = 0.56625 and P = 0.54.
Plugging these values into the formula and calculating the test statistic gives z = (0.56625 - 0.54) / sqrt((0.54 * (1-0.54)) / 800) = 0.56507.
Next, we find the critical value for a one-tailed test at the 0.10 level of significance.
Looking up the value in a standard normal distribution table or using a calculator, we find the critical value to be approximately 1.28.
Since the test statistic, 0.56507, is less than the critical value, 1.28, we fail to reject the null hypothesis.
Therefore, we cannot conclude that the percent of students who play intramural sports receiving a degree within six years is larger than the overall percentage at the 0.10 level of significance.