Question

1) For the t distribution with 16 degrees of freedom, find the value for which the upper tail area is 0.005.

2) For the t distribution with 13 degrees of freedom, calculate P(T < 1.771).

3) In order to estimate the average electric usage per month, a sample of 45 houses were selected and the electric usage determined. The sample mean is 2,000 KWH. Assume a population standard deviation of 101 kilowatt hours. At 90% confidence, compute the margin of error?.

4) In order to estimate the average electric usage per month, a sample of 47 houses were selected and the electric usage determined. The sample mean is 2,000 KWH. Assume a population standard deviation of 142 kilowatt hours. At 99% confidence, compute the upper bound of the interval estimate for the population mean.

5) Consider the population of electric usage per month for houses. The standard deviation of this population is 113 kilowatt hours. How large a sample should be selected to provide a 90% confidence interval for the population mean with a margin of error of 27 or less? (Enter an integer number.)

Answer 1

Answer)

1)

Given degrees of freedom is 16

For degrees of freedom 16 and alpha 0.005

Critical value from t table is = 2.921

2)

From t table, for df 13 and t 1.771

P(t>1.771) = 0.05

So,P(t<1.771) = 1 - 0.05 = 0.95

3)

As the population s.d is known, here we can use standard normal z table to estimate the interval

Critical value z from z table for 90% confidence level is 1.645

Margin of error = z*(s.d/√n) = 1.645*(101/√45) = 24.7674342747

4)

Critical value z for 99% confidence level is 2.58 (from z table)

Margin of error (MOE) = 2.58*142/√47 = 53.4390982851

Upper bound is given by mean + MOE

Mean is 2000

So,

Upper bound = 2053.43909828

5)

Given MOE = 27

critical value z = 1.645 (for 90% confidence level)

S.d = 113

MOE = z*(s.d/√n)

27 = 1.645*(113/√n)

N = 48