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:


27, 22, 11, 19, 20, 19, 25, 21.

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
27	729
22	484
11	121
19	361
20	400
19	361
25	625
21	441
x=164	x2=3522

The sample mean is

Mean   = (x / n) )

= (27+22+11 +19+ 20+ 19+ 25+ 21 / 8 )

= 164 / 8

= 20.5

Mean   = 20.5

The sample standard is S

  S = ( x² ) - (( x)² / n ) n -1

= (3522 ( (164 )² / 8 ) 7

   = ( 3522 - 3362 / 7)

= (160 / 7 )

= 22.8571

= 4.7809

The sample standard is 4.78

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 * (4.78 / 8 )

= 3.997

Margin of error = 3.997

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

+ E

20.5 + 3.997

= 24.497

the upper bound = 24.497