Question

The college bookstore tells prospective students that the average cost of its textbooks is $52 with a σ of $4.50. A group of smart statistics students think that the average cost is much higher. In order to test the bookstore’s claim against their alternative, the students select a random sample of size 100. Assume that the mean from their random sample is $52.80. Use alpha value of 0.05 level to test the hypothesis.

Answer 1

Given that the college bookstore tells prospective students that the average cost of its textbooks is = $52 with a population standard deviation is σ of $4.50.

Now based on the claim the hypotheses are:

since the students select a random sample of size n = 100. Assume that the mean from their random sample is = $52.80.

So, based on the hypothesis it will be a right-tailed test and since the population, the standard deviation is known and the sample size is greater than 30 hence the Z statistic is used to test the hypothesis.

Rejection region:

At a given significance level 0.05 the critical Z-score Zc is computed using excel formula for normal distribution which is =NORM.S.INV(0.95), thus Zc computed as 1.645.

So, reject the Ho if Z > Zc .

Test statistics:

The Test statistic is calculated as:

P-value:

The P-value at the calculated Z score is calculated using excel formula for normal distribution which is =1-NORM.S.DIST(1.78, TRUE), thus P-value computed as 0.0375.

Conclusion:

Since P-value is less than 0.05 and Z is greater than 1.645 hence we can reject the null hypothesis Ho and conclude that there is enough evidence to support the claim that the average cost is much higher.