Question

In a survey, 26 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $42 and standard deviation of $7. Construct a confidence interval at a 90% confidence level.

Give your answers to one decimal place and Interpret your confidence interval in the context of this problem.

Answer 1

Solution :

sample size = n = 26

Degrees of freedom = df = n - 1 = 25

t /2,df = 1.708

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

= 1.708 * (7 / 26)

Margin of error = E = 2.3

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

- E < < + E

42 - 2.3 < < 42 + 2.3

39.7 < < 44.3

We are 90% confidence that people had spent on their child's last birthday gift is between $39.7 and $44.3