In a survey, 13 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 $18. Estimate how much
a typical parent would spend on their child's birthday gift (use a
95% confidence level).
Give your answers to one decimal place. Provide the point estimate
and margin or error.
Answer:
Given,
n = 13
xbar = 39
s = 18
degree of freedom = n - 1
= 13 - 1
= 12
For 95% confidence interval , t(0.025 , 12) = 2.179
Interval = (xbar +/- t*s/sqrt(n))
= 39 +/- 2.179*18/sqrt(13)
= 39 +/-10.9
= (39 - 10.9 , 39 + 10.9)
= (28.1 , 49.9)
Point estimate = xbar = 39
Margin of error = t*s/sqrt(n)
= 2.179*18/sqrt(13)
= 10.9
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