Question

a)For the t distribution with 15 degrees of freedom, calculate P(T < 0.691).

b)Consider the population of electric usage per month for houses. The standard deviation of this population is 132 kilowatt-hours. What is the smallest sample size to provide a 90% confidence interval for the population mean with a margin of error of 34 or less? (Enter an integer number.)

c)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 90% confidence, compute the margin of error?.

d)In order to estimate the average electric usage per month, a sample of 38 houses were selected and the electric usage determined. The sample mean is 2,000 KWH. Assume a population standard deviation of 136 kilowatt hours. At 95% confidence, compute the lower bound of the interval estimate for the population mean.

Answer 1

a) Given that, degrees of freedom = 15

We want to find, P(T < 0.691)

Using Excel we find this probabilitiy :

Excel Command : = 1 - TDIST (0.691, 15, 1) = 0.7499

=> P(T < 0.691) = 0.7499

b) Given that, population standard deviation = 132 killowatt-hours

Margin of error (E) = 34

A 90% confidence level has significance level of 0.10 and critical value is,

We want to find, the sample size (n),

Therefore, required sample size is 41

c) Given that, population standard deviation = 142 killowatt-hours

sample size (n) = 47 and sample mean = 2000 KWH

A 90% confidence level has significance level of 0.10 and critical value is,

We want to find, the margin of error (E),

=> Margin of error = 34.0726

d) Given that, population standard deviation = 136 killowatt-hours

sample size (n) = 38 and smaple mean = 2000 KWH

A 95% confidence level has significance level of 0.05 and critical value is,

We want to compute lower bound of the interval estimate for the population mean,

=> Lower Bound = 1956.76 KWH