Question

The college bookstore tells prospective students that the average cost of its textbooks is $52 with a standard deviation of $4.50. A group of smart statistics students thinks that the average cost is higher. In order to test the bookstore’s claim against their alternative, the students will select a random sample of size 100. Assume that the mean from their random sample is $52.80. Test at 10% significance level.

--> Perform a hypothesis test and state your decision.

Answer 1

Solution :

= 52

=52.80

s = 4.50

n = 100

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 52

H_a : > 52

The significance level is α=0.10 ,and

the critical value for a right-tailed test is t_c​=1.29

Test statistic = t

= ( - ) / s / n

= (52.80- 52) /4.50 / 100

= 1.778

p(Z > 1.778 ) = 1-P (Z < 1.778 ) =0.0393

P-value = 0.0393

= 0.10

p= 0.0393 < 0.10

Reject the null hypothesis .

There is sufficient evidence to suggest that the population mean μ is greater than 52, at the 0.10 significance level