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?

Answer 1

We accept H₀ . We don´t have enough evidence to express the publisher claim is not true

Step by Step explanation:

We must evaluate if the mean of the price of college textbooks is different from the value claimed by the publisher

n < 30 then we must use t - distrbution

degree of freedom n - 1 df = 22 - 1 df = 21

As the question mentions " different " that means, a two-tail test

At 0,01 significance level α = 0,01 α/2 = 0,005

and t(c) = 2,831

Test Hypothesis

Null Hypothesis H₀ μ = μ₀

Alternative hypothesis Hₐ μ ≠ μ₀

To calculate t(s)

t(s) = ( μ - μ₀ ) /σ/√n

t(s) = ( 433,50 - 385 ) / 86,92 / √22

t(s) = 2,6171

Comparing t(c) and t(s)

t(s) < t(c)

Then t(s) is in the acceptance region we accept H₀. We don´t have enough evidence to claim that mean price differs from publisher claim