The electric cooperative needs to know the mean household usage of electricity by its non-commercial customers in kWh per day. Assume that the population standard deviation is 2.3 kWh. The mean electricity usage per family was found to be 15.7 kWh per day for a sample of 1731 families. Construct the 99% confidence interval for the mean usage of electricity. Round your answers to one decimal place.

We are 99% confident that the true mean of electricity comsumption is between (15.6 and 15.8) kWh

Step-by-step explanation:

Information provided

represent the sample mean for the usage of electricity

population mean (variable of interest)

represent the population standard deviation

n=1731 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula if we know the population deviation:

  (1)

The Confidence level provided is  0.99 or 95%, the value of significance is and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that

And replacing we got:

We are 99% confident that the true mean of electricity comsumption is between (15.6 and 15.8) kWh

step-by-step explanation:

the true statements are:

r = set of real numbers

n = set of natural numbers, 1,2,

w = n u{0} = {0,1,}