Twelve different video games showing drug use drug use were observed. The duration times of drug use drug use were recorded, with the times (seconds) listed below. Assume that these sample data are used with a 0.01 0.01 significance level in a test of the claim that the population mean is greater than 80 80 sec. If we want to construct a confidence interval to be used for testing that claim, what confidence level should be used for a confidence interval? If the confidence interval is found to be negative 45.8 −45.8 sec less than < mu μ less than < 260.8 260.8 sec, what should we conclude about the claim?

Null hypothesis:

Alternative hypothesis:

They calculate the following confidence interval:

And since the lower value of the confidence interval is lower than 80 we don't have enough evidence to conclude that the true mean is higher than 80 at the significance level given.

Step-by-step explanation:

Peevious concepts

represent the sample mean

population mean (variable of interest)

s represent the sample standard deviation

n=12 represent the sample size  

represent rhe significance level

Solution to the problem

The confidence interval for the mean is given by the following formula:

  (1)

For this case they want to test the following system of hypothesis:

Null hypothesis:

Alternative hypothesis:

They calculate the following confidence interval:

And since the lower value of the confidence interval is lower than 80 we don't have enough evidence to conclude that the true mean is higher than 80 at the significance level given.

According to the hypothesis:

We are using a level of significance of 0.01, thus, the confidence level is of 1 - 0.01 = 0.99 = 99%.

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