In a survey, 38 people were asked how much they spent on their
child's last birthday gift. The results were roughly bell-shaped
with a mean of $53 and standard deviation of $10.
Calculate, state, and interpret a 95% confidence interval to
estimate the mean amount of money parents spend on their child's
birthday gift. Round to the nearest 100th where
necessary.
Answer: In a survey, 38 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $53 and standard deviation of $10.
Solution:
Calculate, state, and interpret a 95% confidence interval to estimate the mean amount of money parents spend on their child's birthday gift.
n = 38
Mean,x̄ = 53
S.D, s = 10
α = 0.05
df = 38-1 = 37
t_critical = tα/2,df = t(0.025,37)
t critical = 2.0262. (From t table)
a 95% confidence interval to estimate the mean amount:
x̄ ± t(α/2,df) * s/√n
53 ± 2.0262 * 10/√38
53 ± 3.287
(49.713, 56.287)
Therefore, the 95% confidence interval to estimate the mean amount of money parents spend on their child's
birthday gift is ($49.71, $56.29).
Interpretation :
We are 95% confident that, the mean amount of money parents spend on their child's birthday gift lies between $49.71 and $56.29.
Get Answers For Free
Most questions answered within 1 hours.