Question

An irate student complained that the cost of his statistics textbook was too high. He randomly surveyed 37 students and found that the mean amount of money spent on statistics textbooks for these students is $122 with a standard deviation of $7.
(a) Construct a 95% confidence interval for the actual average cost of statistics textbooks.
5.
(b) A statistics professor claims that the average cost of the textbook for her statistics class is $105. What would you tell her?

Answer 1

a)

95% Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 37- 1 ) = 2.028
122 ± t(0.05/2, 37 -1) * 7/√(37)
Lower Limit = 122 - t(0.05/2, 37 -1) 7/√(37)
Lower Limit = 119.67
Upper Limit = 122 + t(0.05/2, 37 -1) 7/√(37)
Upper Limit = 124.33
95% Confidence interval is ( 119.67 , 124.33 )

b)

Since 105 does not contained in confidence interval and all values in confidence interval

are greater than 105

We have sufficient evidence to conclude that the average cost of the textbook for her statistics class

is greater than $105