Question

In a survey, 24 people were asked how much they spent on their child's last birthday gift. The results were roughly bell- shaped with a mean of $ 43 and standard deviation of $17 Construct a confidence interval at a 90% confidence level Give your answers to one decimal place.

Answer 1

Remember that

z =(x - μ)/σ

where

μ=$43

σ=$17

The values of z for a 90% confidence level are equal to

Z=±1.645

so

Find out the values of X

For z=1.645

1.645=(x-43)/17

x-43=27.965

x=27.965+43 ----------> x=70.965 ------> one decimal place -----> x=71.0

For z=-1.645

-1.645=(x-43)/17

x-43=-27.965

x=-27.965+43 ----------> x=15.035 ------> one decimal place ------> x=15.0

therefore

The answer is

The confidence interval is [$15.0,$71.0]