Mathematics

1. Use technology to find the P-value for a right-tailed test with n=11 and test statistic t=1.493. **P-value=?**

2. Use technology to find the P-value for a right-tailed test with n=18 and test statistic t=2.853. **P-value=?**

3. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. A simple random sample of 25 filtered 100 mm cigarettes is obtained, and the tar content of each cigarette is measured. The sample has a mean of 19.2mg and a standard deviation of 3.563.56 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21 mg, which is the mean for unfiltered king size cigarettes. What do the results suggest, if anything, about the effectiveness of the filters?

**Identify the test statistic?**

**Identify the P-value?**

4. The accompanying data table lists the weights of male college students in kilograms. Test the claim that male college students have a mean weight that is less than the 84 kg mean weight of males in the general population. Use a

0.05 significance level. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, and conclusion for the test. Assume this is a simple random sample.

**Calculate the test statistic?**

**Identify the P-value?**

5. The accompanying data table lists measured voltage amounts supplied directly to a family’s home. The power supply company states that it has a target power supply of 120 volts. Using those home voltage amounts, test the claim that the mean is 120 volts. Use a 0.05 significance level.

**Calculate the test statistic?**

**Identify the P-value?**

6. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement? 654, 645, 1190, 611, 537, 551:

**Calculate the test statistic?**

**Identify the P-value?**

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