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