How many hours per week do gamers play video games? A simple random sample of 83 U.S. gamers age 13 or older is given below.

a.) Find a 98% confidence interval for the population average time per week a gamer 13 or older plays video games. (Round answers to two decimal places.)

- Margin of error:
- Lower limit: _ hr/wk
- Upper limit: _ hr/wk

b.) What conditions were met so the results are valid? (Select all that apply.)

- The population standard deviation (\(\sigma\)) is unknown.
- Time per week a gamer 13 or older plays video games needs to be normally distributed.
- Systematic sampling was used.
- The population standard deviation (\(\sigma\)) is known.
- Simple random sample was taken.
- Large enough sample size.
- Time per week a gamer 13 or older plays video games needs to be uniformly distributed.

c.) Interpret: We are 98% confident that the population mean time per week a gamer 13 or older plays video games is between _ hours and _ hours.

To find the confidence interval for the average time per week gamers play video games, we use a formula that involves calculating the standard error and the margin of error.

The conditions that need to be met for the results to be valid include having a simple random sample, a large enough sample size, and a normally distributed population. The confidence interval allows us to state our level of confidence in the range of possible population means.

To find the confidence interval for the population average time per week a gamer 13 or older plays video games, we can use the formula:

Confidence Interval = Sample Mean ± (Z * Standard Error)

First, we need to calculate the standard error, which is the standard deviation of the sample divided by the square root of the sample size.

Once we have the standard error, we can calculate the margin of error by multiplying it by the appropriate Z-score for a 98% confidence level.

Finally, we can calculate the lower and upper limits of the confidence interval by subtracting and adding the margin of error from the sample mean, respectively.

Conditions that need to be met for the results to be valid include having a simple random sample, a large enough sample size, and a normally distributed population.

We can interpret the confidence interval as follows: We are 98% confident that the population mean time per week a gamer 13 or older plays video games is between the lower limit and the upper limit.

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