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 is the data:

19.68, 14.22, 15.42, 11.6,   27.45,   18.44, 20.77,   16.74.
He wishes to test the null hypothesis that the average amount of money people have in their pockets is equal to $20. Calculate the test statistic to two decimal places. Take all calculations toward the answer to three decimal places.

Answer 1

Solution:|
Given in the question
Null hypothesis H0: = 20
Alternate hypothesis Ha: 20
n=8
First we will calculate Sample mean and standard deviation which can be calculated as
Sample mean (Xbar)= Xi/n = (19.68 + 14.22 + 15.42 + 11.6 + 27.45 + 18.44 + 20.77 + 16.74)/8 = 144.32/8 = 18.04
Sample standard deviation(S) = sqrt(((Xi-mean)^2/(n-1)) = sqrt((19.68-18.04)^2 + (14.22-18.04)^2 + (15.42-18.04)^2 + (11.6-18.04)^2 + (27.45-18.04)^2 + (18.44-18.04)^2 + (20.77-18.04)^2 + (16.74-18.04)^2)/7)) = sqrt(163.471/7) = 4.832
Here we will use t test as sample size is small and population standard deviation is unknown so test stat value can be calculated as
Test stat = (Xbar - )/S/sqrt(n) = (18.04-20)/4.832/sqrt(8) = -1.96/1.7085 = -1.15