# Normal distribution and the t distribution

Normal distribution and the t distribution

1. In the following situations, indicate whether you’d use the normal distribution, the t distribution, or neither.
2. The population is normally distributed, and you know the population standard deviation.
3. You don’t know the population standard deviation, and the sample size is 35.
4. The sample size is 22, and the population is normally distributed.
5. The sample size is 12, and the population is not normally distributed.
6. The sample size is 45, and you know the population standard deviation.
7. The prices of used books at a large college bookstore are normally distributed. If a sample of 23 used books from this store has a mean price of \$27.50 with a standard deviation of \$6.75, use Table 10.1 in your textbook to calculate the following for a 95% confidence level about the population mean. Be sure to show your work.
8. Degrees of freedom
9. The critical value of t
10. The margin of error
11. The confidence interval for a 95% confidence leve
12. Statistics students at a state college compiled the following two-way table from a sample of randomly selected students at their college:

Play chess Don’t play chess

Male students 25 162

Female students 19 148

Answer the following questions about the table. Be sure to show any calculations.

1. How many students in total were surveyed?
2. How many of the students surveyed play chess?
3. What question about the population of students at the state college would this table attempt to answer?
4. State Hº and Hª for the test related to this table.
5. Answer the following questions about an ANOVA analysis involving three samples.
6. In this ANOVA analysis, what are we trying to determine about the three populations they’re taken from?
7. State the null and alternate hypotheses for a three-sample ANOVA analysis.
8. What sample statistics must be known to conduct an ANOVA analysis?
9. In an ANOVA test, what does an F test statistic lower than its critical value tell us about the three populations we’re examining?

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