Question

Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money that people spend in thrift shops. He takes a small sample of 8 individuals and asks them to report how much money they had in their pockets the last time they went shopping at a thrift store. Here are the data:

11, 23, 26, 28, 30, 11, 11, 28.

Find the upper bound of a 95% confidence interval for the true mean amount of money individuals carry with them to thrift stores, to two decimal places. Take all calculations toward the final answer to three decimal places.

Answer 1

First the computations are made here using the following table:

X	(X - Mean(X))^2
11	100
23	4
26	25
28	49
30	81
11	100
11	100
28	49
168	508

The last row in the table contains the sum of the respective column.

The sample mean and sample standard deviation here are computed as:

For n - 1 = 7 degrees of freedom, we have from t distribution tables here:
P( t₇ < 2.365 ) = 0.975

Therefore, P( -2.365 < t₇ < 2.365) = 0.95

Therefore the upper bound of the 95% confidence interval here is obtained as:

Therefore 28.12 is the required upper bound of the 95% confidence interval for the true mean amount of money individuals carry with them to thrift stores