Question

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 95 % confidence interval estimate of mean, the mean duration of game play.

4058 3876 3854 4030 4319 4805 4665 4025 5014 4816 4331 4312

What is the confidence interval estimate of the population mean?

_ <mean<_

Answer 1

Solution:

x	dx = x - A = x - 4342	dx2
4058	-284	80656
3876	-466	217156
3858	-488	238144
4030	-312	97344
4319	-23	529
4805	463	214369
4665	323	104329
4025	-317	100489
5014	672	451584
4816	474	224676
4331	-11	121
4312	-30	900
x = 52105	dx = 1	dx2 = 1730297

a ) The sample mean is

=  x / n

= (4058+3876+3854+4030+4319+4805+4665+4025+5014+4816+4331+4312 / 12 )

= 52105 / 12

= 4342 .0833

= 4342

The sample standard is S

S = ( dx² ) - (( dx )² / n ) / 1 -n )

= ( 1730297 ( (- 1 )² / 12 ) / 11

   = ( 1730297 -10.0833 / 11 )

= (1730296.9167 / 11 )

= 157299.7197

= 396.6103

= 397

The sample standard is = 397

Given that,

= 4342

s = 397

n = 12

Degrees of freedom = df = n - 1 = 12 - 1 = 11

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,11 = 2.201

Margin of error = E = t_/2,df * (s /n)

= 2.201 * ( 397 / 12)

= 252.2

The 95% confidence interval estimate of the population mean is,

- E < < + E

4342 - 252.2 < < 4342 + 252.2

4089.8 < < 4594.2

(4089.8, 4594.2 )