1. IQ tests are designed to yield results that are approximately normally distributed. A reporter is interested in estimating the average IQ of employees in a large high-tech firm in California. She gathers the IQ information on 22 employees of this firm and records the sample mean IQ as 106 with a standard deviation of 15.
   1. What is the best point estimate for the population mean?
   2. What is the 95% confidence interval for the population mean?
   3. Interpret your confidence interval limits

1. The U.S. department of education reported that in 2007, 67% of students enrolled in college or a trade school within 12 months of graduating from high school. In 2010, a random sample of 160 individuals who graduated from high school 12 months prior was selected. From this sample, 102 students were found to be enrolled in college or trade school.
   1. What is your point estimate of the sample proportion of students enrolled in college or a trade school within 12 months of graduating from high school in year 2010?
   2. What is the standard error of the sample proportion?
   3. Find the margin of error using a 90% confidence coefficient?
   4. Construct a 90% confidence interval to estimate the actual proportion of students enrolled in college or a trade school within 12 months of graduating from high school in 2010.
   5. Based on this sample, is there any evidence that this proportion has changed since 2007?
2. A research analyst disputes a trade groups prediction that back-to-school spending will average $606.40 per family this year. She believes that average back-to-school spending will significantly higher from this amount. She decided to conduct a test on the basis of a random sample of 36 households with school-age children. She calculates the sample mean as $622.85. She also believes that back-to-school spending is normally distributed with a population standard deviation of $65.
   1. State the null hypothesis and the alternate hypothesis.
   2. State the decision rule at the 5% level of significance for the critical value method.
   3. Compute the value of test statistic.
   4. What is your decision regarding null hypothesis by the Critical value method?
   5. What is the p-value? Use the p value to draw your conclusion regarding the null hypothesis.

1. According to a recent study, todays population of undergraduates studies an average of 14 hours per week (national average). A random sample of 16 students from a normal population shows an average study hours per week as 16.37 with a standard deviation of 7.22. Conduct a test to find if the mean study time of students from this sample differs from the national average of 14 hours per week? Use the P value method to draw your conclusion with 5% level of significance.
2. Many people who own digital cameras prefer to have pictures printed. In a preliminary study to determine spending patterns, a random sample of 8 digital camera owners and 8 standard camera owners were surveyed and asked how many pictures they printed in the past month. The results are presented here. Can we infer that the two groups differ in the mean number of pictures that are printed? Use the 5% level of significance and draw your conclusions by both P value method as well as the Critical value method.

Digital	Standard
15	0
12	24
23	36
31	24
20	0
14	48
12	0
19	0

Summary Statistics of the data in Question 5 above to be used in the formula as an option

	Digital	Standard
Mean	18.25	16.5
Standard deviation	6.5	19.2
Sample size	8	8