Twelve different video games showing substance use were obse

Twelve different video games showing substance use were observed and the duration times of game play (in seconds) are listed below. The design of the study justifies the assumption that the sample can be treated as a simple random sample. Use the data to construct a 99% confidence interval estimate of ?, the mean duration of game play. 4053 3889 3862 4037 4325 4822 4654 4026 5012 4824 4343 4308 What is the confidence interval estimate of the population mean ?? Please show how to get the sample standard deviation by steps? I am only confuse to how to get the answer for s. Thanks.

Solution

x

x-meanx

(x-meanx)²

4053

-293.25

85995.56

3889

-457.25

209077.6

3862

-484.25

234498.1

4037

-309.25

95635.56

4325

-21.25

451.5625

4822

475.75

226338.1

4654

307.75

94710.06

4026

-320.25

102560.1

5012

665.75

443223.1

4824

477.75

228245.1

4343

-3.25

10.5625

4308

-38.25

1463.063

total

52155

1722208

Mean = ? x/n =52155/12=4346.25

? ( xi - x )² = 1722208

Sample standard deviation = s = sqrt [ ? ( xi - x )² / ( n - 1 ) ]

=sqrt(1722208/11) = 395.682

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation

395.682

Sample Mean

4346.25

Sample Size

12

Confidence Level

99%

Intermediate Calculations

Standard Error of the Mean

114.2236

Degrees of Freedom

11

t Value

3.1058

Interval Half Width

354.7564

Confidence Interval

Interval Lower Limit

3991.49

Interval Upper Limit

4701.01

	x	x-meanx	(x-meanx)2
	4053	-293.25	85995.56
	3889	-457.25	209077.6
	3862	-484.25	234498.1
	4037	-309.25	95635.56
	4325	-21.25	451.5625
	4822	475.75	226338.1
	4654	307.75	94710.06
	4026	-320.25	102560.1
	5012	665.75	443223.1
	4824	477.75	228245.1
	4343	-3.25	10.5625
	4308	-38.25	1463.063
total	52155		1722208