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:

29.34, 24.88, 28.5, 12.02,   13.45,   13.41, 10.03,   25.09.

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
29.34	860.8356
24.88	619.0144
28.5	812.25
12.02	144.4804
13.45	180.9025
13.41	179.8281
10.03	100.6009
25.09	629.5081
---	---
x=156.72	x2=3527.42

The sample mean is

Mean   = (x / n) )

= (29.34+ 24.88 +28.5+ 12.02+ 13.45 + 13.41+ 10.03 + 25.09/ 8 )

= 156.72 / 8

= 19.5

Mean   = 19.59

The sample standard is S

  S = ( x² ) - (( x)² / n ) n -1

= (3527.42( (155 )² / 8 ) 7

   = ( 3527.42 - 3070.1448 / 7)

= (457.2752 / 7 )

= 65.325

= 8.0824

The sample standard is 8.082,

= 20

Test statistic = t

= ( - ) / s / n

= (19.59 - 20) / 8.082/ 8

= - 0.143

Test statistic = t = - 0.14