Confidence interval estimate

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

9595​%

confidence interval estimate of

muμ​,

the mean duration of game play.

4050

3890

3854

4020

4310

4804

4650

4033

5005

4828

4324

4309

What is the confidence interval estimate of the population mean

muμ​?

nothingless than<muμless than<nothing

​(Round to one decimal place as​ needed.)

Answer 1

To compute the 95% confidence interval we will first need to compute the mean and standard deviation of our sample: the mean is 4339.75 and the standard deviation is 394.66.

Since we do not know the population standard deviation, to compute the 95% confidence interval we will be using a critical t value with 11 degrees of freedom (sample size of 12 - 1).

The 95% confidence interval = sample mean +/- critical t value * standard error

The critical t value from the tables is: 2.201 (since 95% confidence level, use value corresponding to upper tail probability of 0.025).

The standard error = standard deviation (394.66)/square root of sample size (12) = 113.93

Putting it all together, the 95% confidence interval = 4339.75 +/- 2.201 * 113.93 = (4088.99,4590.51)