In: Statistics and Probability
In a survey, 26 people were asked how much they spent on their
child's last birthday gift. The results were roughly bell-shaped
with a mean of $42 and standard deviation of $7. Construct a
confidence interval at a 90% confidence level.
Give your answers to one decimal place and Interpret your
confidence interval in the context of this problem.
Solution :
sample size = n = 26
Degrees of freedom = df = n - 1 = 25
t
/2,df = 1.708
Margin of error = E = t/2,df
* (s /
n)
= 1.708 * (7 /
26)
Margin of error = E = 2.3
The 90% confidence interval estimate of the population mean is,
- E <
<
+ E
42 - 2.3 <
< 42 + 2.3
39.7 <
< 44.3
We are 90% confidence that people had spent on their child's last birthday gift is between $39.7 and $44.3