Question

How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 61 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on the number of tissues used during a cold:

X-bar (mean): 47

s= 20

α= 0.01

Conduct a hypothesis test based on the data and be sure to write out all of the steps (hypothesis, test statistic, statistical decision and practical decision)

Answer 1

Given that the sample size is and sample mean , sample standard deviation .
The hypotheses are

Since the sample size is very large, we use z-distribution.

The test statistics is

The P-value of the test is

Since the p-value is , statistical decision is we reject the null hypothesis.

Conclusion: We are 99% confident that the average number of tissues during a cold is different from 61.

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For a left side test (one sided), the hypotheses are

The P-value of the test is

Since the p-value is , statistical decision is we reject the null hypothesis.

Conclusion: We are 99% confident that the average number of tissues during a cold is less than 61.

You can use either of these tests.