3. A sample of 312 grades on mathematics test given nationwide reveals that the sample mean of 560, and the sample variance = 14400.0. Construct a 99 % confidence interval for population mean and interpret your findings.

4. In a study of childhood abuse in psychiatric patients, it was found that in a sample of 947 patients, 166 reported histories of physical and/or sexual abuse.

Find proportion of the population with historical child abuse.

Construct 90 % confidence interval for this population proportion

5. Using = 0.01 find the critical value of t when sample size is equal 15 for the following

hypothesis testing:

H0: = 50 HA: 50

6. In a test of the hypothesis that females smile at others more than males do, female and males were videotaped while interacting and the number of smiles emitted by each sex was noted. Using the following number of smiles in a 5-minute interaction, test the null hypothesis that there are no sex differences in the number of smiles:

MALES: 8 11 13 4 2

FEMALES :15 19 13 11 18