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: 12, 31, 17, 18, 22, 36, 15, 13. 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

Solution:

x	x2
12	144
31	961
17	289
18	324
22	484
36	1296
15	225
13	169
x=164	x2=3892

The sample mean is

Mean   = (x / n) )

= (12 + 31 + 17+ 18 +22 +36 + 15 +17 / 8 )

= 164 / 8

= 20.5

Mean   = 20.5

The sample standard is S

  S = ( x² ) - (( x)² / n ) n -1

= (3892 ( (164 )² / 8 ) 7

   = ( 3892- 3362 /7)

= (530 / 7 )

= 75.7143

= 8.7014

The sample standard is 8.70

Degrees of freedom = df = n - 1 = 8 - 1 = 7

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,7 = 2.365

Margin of error = E = t_/2,df * (s /n)

= 2.365 * (8.70 / 8 )

= 7.274

Margin of error =7.274

The 95% confidence interval estimate of the population mean is,

- E < < + E

20.5 - 7.274 < < 20.5 +7.274

13.225 < < 27.774

(13.225, 27.774 )