Exhibit 9-7
A random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a variance of 64. We are interested in determining whether the average grade of the population is significantly more than 75. Assume the distribution of the population of grades is normal.
-Refer to Exhibit 9-7. At 95% confidence, it can be concluded that the average grade of the population
A)is not significantly greater than 75
B)is significantly greater than 75
C)is not significantly greater than 78.6
D)is significantly greater than 78.6

Question

Quizplus · Accepted Answer

We need to perform a one-sample t-test to determine if the sample mean of 78.6 is significantly different from our null hypothesis of 75. The formula for the t-test is:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Assuming a two-tailed test and a significance level of 0.05, we can refer to a t-distribution table with 15 degrees of freedom (sample size - 1), giving us a critical value of 2.131.

plugging in our values, we get:

t = (78.6 - 75) / (sqrt(64/16))
t = 3 / 2
t = 1.5

Our calculated t-value of 1.5 is less than the critical value of 2.131, so we fail to reject the null hypothesis. Therefore, we conclude that at 95% confidence, the average grade of the population is significantly greater than 75.

Exhibit 9-7 A Random Sample of 16 Statistics Examinations from a Large