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.
Solution :
Given that,
x | x2 |
12 | 144 |
31 | 961 |
17 | 289 |
18 | 324 |
22 | 484 |
36 | 1296 |
15 | 225 |
13 | 169 |
∑x=164 | ∑x2=3892 |
Mean ˉx=∑xn
=12+31+17+18+22+36+15+13/8
=164/8
=20.5
Sample Standard deviation S=√∑x2-(∑x)2nn-1
=√3892-(164)28/7
=√3892-3362/7
=√530/7
=√75.7143
=8.7014
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 = t0.025,7 =2.365
Margin of error = E = t/2,df * (s /n)
= 2.365 * (8.70 / 8)
= 7.273
Margin of error = 7.273
The 95% confidence interval estimate of the population mean is,
+ E
20.5 + 7.273
The upper bound = 27.773
Get Answers For Free
Most questions answered within 1 hours.