In a survey, 30 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $37 and standard deviation of $13. Construct a confidence interval at a 98% confidence level. Give your answers to one decimal place.
Solution :
Given that,
Point estimate = sample mean = = 37
sample standard deviation = s = 13
sample size = n = 30
Degrees of freedom = df = n - 1 = 29
At 98% confidence level the t is ,
= 1 - 98% = 1 - 0.98 = 0.02
/ 2 = 0.02 / 2 = 0.01
t /2,df = t0.01,29 = 2.462
Margin of error = E = t/2,df * (s /n)
= 2.462 * (13 / 30)
= 5.8
The 98% confidence interval estimate of the population mean is,
- E < < + E
37 - 5.8 < < 37 + 5.8
31.2 < < 42.8
(31.2, 42.8)
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