Question

Suppose you were attending a university where students hated the bookstore and their aggressively high prices. Suppose further that a student organization goes to the bookstore and argues that prices of text books are exceeding $150 per class. At such outrageous prices, students can no longer afford to go to school. The college bookstore claims that an average student pays $101.75 per class for texts (far below the stated claim of $150). A student group randomly selects ten courses from the catalog and finds the costs for each: $140, $125, $150, $124, $143, $170, $125, $94, $127, and $53.

a. Is that enough to justify a claim that the bookstore is underestimating the amount spent? Make sure that you show your work.

b. Students decide to take a sample from one more class and find that this class has a textbook cost of $195. Does adding this observation to the other 10 observations change your answer to part (a) above?

Answer 1

Here

hypothesis are

Null Hypothesis :H₀ : = $ 101.75

Alternative Hypothesis :H_a : > $ 101.75

Here n = 10

sample mean amount of ten courses = $ 125.1

sample standard deviation = s = $ 32.23

Here

standard error of sample mean = s/sqrt(n) = 32.23/sqrt(10) = $10.192

Test statistic

t = (125.1 - 101.75)/10.192 = 2.291

Here critical test statistic

t_critical = 2.685

so here as t < t(Critical) so it is not enough justify a claim that the bookstore is underestimating the amount spent

(b) Now adding one more sample value

now,

Here n = 11

sample mean amount of ten courses = $ 131.4545

sample standard deviation = s = $ 37.136

Here

standard error of sample mean = s/sqrt(n) = 37.136/sqrt(11) = $11.197

Test statistic

t = (131.4545 - 101.75)/11.197 = 2.653

Here critical test statistic

t_critical = 2.634 for dF = 10

so here as t >n t(Critical) so here in this case it is enough to justify a claim that the bookstore is underestimating the amount spent