Question

In a random sample of 7 residents of the state of Texas, the mean waste recycled per person per day was 2.7 pounds with a standard deviation of 0.72 pounds. Determine the 99% confidence interval for the mean waste recycled per person per day for the population of Texas. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 2.7

sample standard deviation = s = 0.72

sample size = n = 7

Degrees of freedom = df = n - 1 = 7 - 1 = 6

At 99% confidence level the t is,

= 1 - 0.99 = 0.01

/2 = 0.005

t _/2,df = t 0.005,6 = 3.707

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

= 3.707 * ( 0.72 / 7 )

Margin of error = E = 1.009

The 99% confidence interval estimate of the population mean is,

- E < < + E

2.7 - 1.009 < < 2.7 + 1.009

1.691 < < 3.709

( 1.691, 3.709)