Question

1a. The right front tire of 9 cars in a department store parking lot were measured and found to have an average tread depth of 0.35 inches, with a sample standard deviation (s) of 0.07 inches. You will making calculations for the 90% confidence interval of the population mean. For question 8, give the (positive) alpha/2 value (from the t-tables) you will be using in setting up your confidence interval. For question 9, give your calculated answer for the lowest value of the 90% confidence interval of the population mean. For question 10 give your calculated answer for the highest value of the 90% confidence interval of the population mean.  Round your calculated lowest and highest interval levels to the hundredths place
1b. Give your answer here for the lowest value of the 90% confidence interval of the population mean (refer to question 1a above).  Round your answer to the hundredths place.
1c. Give your answer here for the highest value of the 90% confidence interval of the population mean (refer to question 8 above). Round your answer to the hundredths place.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 0.35

sample standard deviation = s = 0.07

sample size = n = 9

Degrees of freedom = df = n - 1 = 9 - 1 = 8

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t0.05,8 = 1.860

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

= 1.860 * ( 0.07/ 9)

Margin of error = E = 0.04

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

  ± E  

= 0.35   ± 0.04

= ( 0.31, 0.39 )

lowest value = 0.31

highest value = 0.39