Question

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?

Answer 1

Answer:

Null hypothesis: $\mu \leq 80$

Alternative hypothesis: $\mu>80$

They calculate the following confidence interval: $45.8 \leq \mu \leq 260.8$

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

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n=12 represent the sample size  

$\alpha=0.01$ represent rhe significance level

Solution to the problem

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

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$   (1)

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

Null hypothesis: $\mu \leq 80$

Alternative hypothesis: $\mu>80$

They calculate the following confidence interval: $45.8 \leq \mu \leq 260.8$

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.

Answer 2

According to the hypothesis:

• A confidence level of 99% should be used.
• The lower bound of the confidence interval is below 80, which means that we cannot conclude that the population mean is greater than 80 sec.

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

• We are testing if the population mean is greater than 80 sec.
• The confidence interval is between -45.8 sec and 260.8 sec.

• The lower bound is below 80, that it, it would be reasonable to find a mean time below 80 sec, thus, we cannot conclude that the population mean is greater than 80 sec.

A similar problem is given at https://brainly.com/question/24989605