Question

Sixteen new textbooks in the bookstore, had prices with a mean of $70.41 and a standard deviation of $19.70. Use a 0.05 significance level to test the claim that the mean price of a textbook at this college is less than $75? Given: n=16, x=$70.41, s=$19.70, alpha= 0.05, mean= $75.

Answer 1

Given: n=16, x=$70.41, s=$19.70, alpha= 0.05, mean= $75.

Claim is that the mean price of a textbook at this college is less than $75, it is alternate hypothesis.

For null hypothesis, we will assume that the mean price of a textbook at this college is equal to $75

Ho :- mean is equal to 75

Ha:- mean is less than 75

Population standard deviation is unknown and sample size is less than 30, so we will use t distribution for hypothesis testing

Formula for t statistics is given as

setting the given values, we get

this gives us

t = -4.59/4.925 = -0.9320

Degree of freedom = n-1 = 16-1= 15

Using the df = 15 and t value = -0.9320 with signifance level of 0.05 in the t distribution table for one tailed testing, we get

p value = 0.1831

it is clear that the p value is greater than 0.05 level of significance, we failed to reject the null hypothesis as result is insignificant.

Thus, we can conclude that we have insufficient evidence to support the claim that the mean price of a textbook at this college is less than $75