Question

In a survey, 16 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $46 and standard deviation of $6. Estimate how much a typical parent would spend on their child's birthday gift (use a 90% confidence level).

Give your answers to one decimal place. Provide the point estimate and margin or error.

±±

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 46

sample standard deviation = s = 6

sample size = n = 16

Degrees of freedom = df = n - 1 = 16-1 = 15

At 90% confidence level

= 1-0.90% =1-0.9 =0.10

/2 =0.10/ 2= 0.05

t/2,df = t0.05,63 = 1.75

t /2,df = 1.75

Margin of error = E = t/2,df * (s /n)

=1.75 * (6 / 16)

Margin of error = E =2.63

The 90% confidence interval estimate of the population mean is,

E

46 ​​​​​​​ 2.63

(43.4,48.6)