In a survey, 16 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $39 and standard deviation of $15. Construct a confidence interval at a 99% confidence level. Give your answers to one decimal place. ±
Solution :
sample size = n = 16
Degrees of freedom = df = n - 1 = 16 - 1 = 15
t
/2,df = 2.947
Margin of error = E = t/2,df
* (s /
n)
= 2.947 * (15 /
16)
Margin of error = E = 11.05
The 99% confidence interval estimate of the population mean is,
- E <
<
+ E
39 - 11.05 <
< 39 + 11.05
27.95 <
< 50.05
(28, 50.1)
The 99% confidence interval is from 28 to 50.1
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