A study was conducted in order to estimate , the mean number of weekly hours tha

Question

A study was conducted in order to estimate , the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be = 3.6 hours. A similar study conducted a year earlier estimated that , the mean number of weekly hours that U.S. adults use computers at home, was 8 hours. We would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean has changed since the previous year. Using a 95% confidence interval of (7.7, 9.3), our conclusion is that:

the current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval.

the current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.

None of the above. The only way to reach a conclusion is by finding the p-value of the test.

Which of the following facts about the p-value of a test is correct?

The p-value is calculated under the assumption that the null hypothesis is true.

The smaller the p-value, the more evidence the data provide against H0.

The p-value can have values between -1 and 1.

All of the above are correct.

Just (A) and (B) are correct.

Explanation / Answer

Our conclusion:

The current study does not provide significant evidence that mean number of weely hours has changed over the past year , since 8 falls inside the confidence interval .

Facts about p value that are correct

The p value is calculated under the assumption that null hypothesis is true

The smaller the p value , more evidence the data provide against null hypothesis

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