39: Suppose that the amount of time teenagers spend on the internet is normally distributed with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours. a. Determine the 95% confidence interval estimate of the population mean. b. Interpret what the confidence interval estimate tells you.

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a) The 95% confidence interval estimate of the population mean is between 6.206 hours and 6.794 hours.

b) The confidence interval means that we are 95% sure that the true population mean for the amount of time teenagers spend on the internet is between 6.206 hours and 6.794 hours.

Step-by-step explanation:

a)Confidence interval:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

In which is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 6.5 - 0.294 = 6.206 hours.

The upper end of the interval is the sample mean added to M. So it is 6.5 + 0.294 = 6.794 hours.

The 95% confidence interval estimate of the population mean is between 6.206 hours and 6.794 hours.

b)Interpretation:

The confidence interval means that we are 95% sure that the true population mean for the amount of time teenagers spend on the internet is between 6.206 hours and 6.794 hours.

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step-by-step explanation:

a.)the line for function b is steeper