Homework

Homework Business Statistics II - STAT222 Summer 2015 (Due on 12/8/2015) Name: 1-___________________________________________ Student ID ________________ 2-___________________________________________ Student ID ________________ 3-___________________________________________ Student ID ________________ 4-___________________________________________ Student ID ________________ Instructions - This homework is a group homework (group of 4 students maximum) It counts for 5% of your total grade. Show All the Steps Question One: Read the Problem [2 points] A real estate agent believes that home with swimming pools take longer to sell than home without swimming pools. A random sample of each type of recently sold homes was taken where the number of days on the market is recorded. Results are: Sample mean Sample Standard deviation Sample size Homes with pool 77 days 8.4 days 19 Homes without pool 65 days 7.2 days 23 Assuming that the populations are normally distributed: a. [1 point] What assumption we can make about the population variances: equal or unequal? Interpret your results? b. [1 point] Conduct the appropriate hypothesis test to determine if the real estate agent is correct. Use the 0.05 level of significance. Question Two: Read the Problem [2 points] A maker of toothpaste is interested in testing whether the proportion of adults (over age 18) who use its toothpaste and have no cavities within a six-month period is any different from the proportion of children (18 and under) who use the toothpaste and have no cavities within a six-month period. To test this, it has selected a sample of adults and a sample of children randomly from the population of those customers who use their toothpaste. The following results were observed. Sample size Number with 0 cavities Adults 100 83 Children 200 165 a. [1 point] Based on these sample data and using a significance level of 0.05, what conclusion should be reached? What is the p-value. b. [1 point] Develop and interpret the desired 95 percent confidence interval estimate. Question Three: Read the Problem [1 points] Random samples from two normal populations produced the following statistics: ?? = 10 ?? =10 ?? = 28 ?? =19 a. [1 point] Estimate with 95% confidence the ratio of the two population variances.