Question

A project in Environment Studies requires you to study monthly home electrical usage.  You randomly called 50 homes in Irvine asking how much each home pays on average for electricity during the fall. You were able to get only 20 responses with data displayed below.  The population is assumed to be normally distributed. α = 0.01

68           85           60           72           42           55           40           64           67           60

52           72           110        70           68           56           35           75           50           84

Fill in the blank:  We are ___________% confident that the interval from _________ to __________ actually contains _______________________________________________.

Answer 1

The sample size is n = 20 The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	X	X2
	68	4624
	85	7225
	60	3600
	72	5184
	42	1764
	55	3025
	40	1600
	64	4096
	67	4489
	60	3600
	52	2704
	72	5184
	110	12100
	70	4900
	68	4624
	56	3136
	35	1225
	75	5625
	50	2500
	84	7056
Sum =	1285	88261

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

The number of degrees of freedom are df = 20 - 1 = 19 , and the significance level is α=0.01.

Based on the provided information, the critical t-value for α=0.01 and df = 19 degrees of freedom is t_c = 2.861

The 99% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 99 % confidence for the population mean μ is

CI = (64.25 - 11.08, 64.25 + 11.08)

CI = (53.17, 75.33)

which completes the calculation.

We are 99% confident that the interval from 53.17 to 75.33 actually contains the amount home pays on average for electricity during the fall.