Question

The submissions for all hypothesis testing problems must have all six of the hypothesis testing steps.

1. The director of the admissions at a large university advises parents of incoming students about the cost of textbooks during a typical semester. He selected a sample of 100 students and recorded their textbook expenses for the semester. He then computed a sample mean cost of $315.40 and a sample standard deviation of $43.20. Using the .01 level of significance, is there evidence that the population mean is above $300?

Please write the solution on here, as its hard for me to read if you wrote the answer on paint

Answer 1

The hypothesis being tested is:

H₀: µ = $300

H_a: µ > $300

We have:

x = $315.40

µ = $300

s = $43.20

n = 100 students

The test statistic, t = (x - µ)/s/√n

t = (315.40 - 300)/43.20/√100

t = 3.565

The degrees of freedom is, df = n - 1 = 100 - 1 = 99

The p-value for df = 99 and alpha = 0.01 is 0.0003.

Since the p-value (0.0003) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the population mean is above $300.