Question

In a survey, 15 people were asked how much they spent on their
child's last birthday gift. The results were roughly bell-shaped
with a mean of $35 and standard deviation of $20. Construct a
confidence interval at a 98% confidence level.

Give your answers to one decimal place.

Answer #1

Sample size n = 15

Sample mean Xbar = $ 35

Sample standard deviation s = $ 20

The 98% confidence interval for population mean

xbar - E < < xbar + E

Where E = t_{a/2}*( s/√n)

For a = 0.02 and d.f = n -1 = 14

t_{a/2 , n -1} = t_{0.01 , 14}

Using t table

t_{0.01,14} = 2.624

E = 2.624*(20/√15)

E = 13.55

35 - 13.55 < < 35 + 13.55

21.4 < < 48.6

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