Question

A publishing company claims that in fall 2019, the average price of college textbooks for a single semester is $385. Suppose you decide to collect data from a random sample of students to assess whether the publisher's claim is reasonable, and you find that in a random sample of 22 college students, the mean price of textbooks for the fall 2019 semester was $433.50 with a standard deviation of $86.92.  

At the 0.01 significance level, is there sufficient evidence to conclude that the mean price of college textbooks for a single semester is different from the value claimed by the publisher?  We can assume that the population of textbook prices are normally distributed.

What is the P-value? Round to three decimal places.

Answer 1

Solution :

This is a two tailed test.

The null and alternative hypothesis is,

Ho: $\mu$ $=$ $385

Ha: $\mu$ $\neq$ $385

The test statistics,

t =( $\bar x$ - $\mu$ )/ (s /$\sqrt{}$n)

= ( 433.50 - 385 ) / ( 86.92 /$\sqrt{}$ 22 )

= 2.617

P-value = 0.016

The p-value is p = 0.016 > 0.01, it is concluded that the null hypothesis is fail to rejected.

There is not sufficient evidence to conclude that the mean price of college textbooks for a single semester is different from the value claimed by the publisher.