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August 30, 2015
Posted by **Steven ** on Tuesday, December 17, 2013 at 5:23pm.

• A new television series must prove that it has more than 25% of the viewing audience after its initial 13-week run in order to be judged successful. Assume that in a sample of 400 households, 112 were watching the series. At a 10% level of significance, can the series be judged successful based on this information? State any assumptions you make. Clearly state the null and alternate hypotheses.

• A bath soap manufacturing process is designed with the expectation that each batch prepared in the mixture department will produce a mean of 120 bars of soap per batch. A mean over or under this standard is undesirable. A sample of ten batches shows the following numbers of bars of soap:

108, 118, 120, 122, 119, 113, 124, 122, 120, 123

Use a 5% level of significance and test to see the null hypothesis H0: =120 should be rejected.

State any assumptions you make. Clearly state the alternate hypotheses

- statistics 4. -
**MathGuru**, Tuesday, December 17, 2013 at 6:42pmHere are a few ideas to get you started.

First problem:

Try a one-sample z-test.

Formula:

z = (sample mean - population mean)/(standard deviation divided by the square root of sample size)

Your data:

sample mean = 2.6

population mean = 2.5

standard deviation = 0.5

sample size = 40

Plug values into the formula and calculate the z-test statistic.

Compare to the critical value for a one-tailed test at .05 level of significance (you can determine this using a z-table). If the test statistic exceeds the critical value, reject the null. If the test statistic does not exceed the critical value, do not reject the null. You will then be able to answer the question about the manufacturer's claim.

Second problem:

You can use a one-sample proportional z-test for your data. (Test sample proportion = 112/400 or .28) Find the critical value in the appropriate table at .10 level of significance for a one-tailed test. Compare the test statistic you calculate to the critical value from the table. If the test statistic exceeds the critical value, reject the null. If the test statistic does not exceed the critical value, do not reject the null. You can draw your conclusions from there.

Third problem:

You will need to calculate mean and standard deviation for the data. Then use a one-sample t-test or a one-sample z-test. You can probably use the t-test since the sample size is small unless otherwise instructed.

I'll let you take it from here.