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:

28.24, 28.39, 32.85, 19.96,   24.74,   13.88, 17.9,   24.41.

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:

x	x2
28.24	797.4976
28.39	805.9921
32.85	1079.1225
19.96	398.4016
24.74	612.0676
13.88	192.6544
17.9	320.41
24.41	595.8481
∑x=190.37	∑x2=4801.9939

Mean ˉx=∑xn

=28.24+28.39+32.85+19.96+24.74+13.88+17.9+24.41 / 8

=190.37 / 8

=23.7962
Mean ˉx= 23.80

Sample Standard deviation S=√∑x2-(∑x⁾²nn-1

=√( 4801.9939-(190.37)² 8 ) 7

=√(4801.9939-4530.0921 ) 7

=√271.9018 / 7

=√38.8431

=6.2324

Sample Standard deviation S= 6.23

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 20

H_a :     20

Test statistic = t

= ( - ) / s / n

= (-20) / 6.23/ 8

= 1.725

Test statistic = t =  1.72

P-value =0.1281