Question

In: Math

Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money...

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.

Solutions

Expert Solution

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


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