Question

Assume that a sample is used to estimate a population mean μ. Find the 99.5% confidence interval for a sample of size 35 with a mean of 40.4 and a standard deviation of 10.4. Enter your answer as an open-interval (i.e., parentheses) accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

99.5% C.I. = ______

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

Given that,

= 40.4

s = 10.4

n = 35

Degrees of freedom = df = n - 1 = 35 - 1 = 34

At 99.5% confidence level the t is ,

= 1 - 99.5% = 1 - 0.995 = 0.005

/ 2 = 0.005 / 2 = 0.0025

t /2,df = t0.0025,34 =3.002

The critical value =3.002

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

= 2.797 * (10.4 / 35)

= 5.277

Margin of error = 5.277

The 99.5% confidence interval estimate of the population mean is,

- E < < + E

40.4 - 5.277 < < 40.4 + 5.277

35.123 < < 45.677

(35.123, 45.677 )