Normal distribution and the t distribution

- In the following situations, indicate whether you’d use the normal distribution, the t distribution, or neither.
- The population is normally distributed, and you know the population standard deviation.
- You don’t know the population standard deviation, and the sample size is 35.
- The sample size is 22, and the population is normally distributed.
- The sample size is 12, and the population is not normally distributed.
- The sample size is 45, and you know the population standard deviation.
- 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.
- Degrees of freedom
- The critical value of t
- The margin of error
- The confidence interval for a 95% confidence leve
- 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.

- How many students in total were surveyed?
- How many of the students surveyed play chess?
- What question about the population of students at the state college would this table attempt to answer?
- State Hº and Hª for the test related to this table.
- Answer the following questions about an ANOVA analysis involving three samples.
- In this ANOVA analysis, what are we trying to determine about the three populations they’re taken from?
- State the null and alternate hypotheses for a three-sample ANOVA analysis.
- What sample statistics must be known to conduct an ANOVA analysis?
- 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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