Exam 22: Binomial Distribution and Normal Approximation

To construct a bootstrap confidence interval estimate for the population mean,you will resample the initial sample by selecting n values with replacement from the n values in the initial sample for m different times.

SCENARIO 12-18 The director of transportation of a large company is interested in the usage of the company's van pool program.She surveyed 129 of her employees on the usage of the program before and after a campaign to convince her employees to use the service and obtained the following: She will use this information to perform test using a level of significance of 0.05. -Referring to Scenario 12-18,the director now wants to know if the proportion of employees who use the service before the campaign and the proportion of employees who use the service after the campaign are the same.Which test should she use?

You can use the Poisson distribution to approximate the binomial distribution when the sample size is large and the probability of an event of interest is very small.

SCENARIO 16-15 Given below are the average prices for three types of energy products for five consecutive years. -Referring to Scenario 16-15,what is the Laspeyres price index for the group of three energy items in year 3 for a family that consumed 15 units of electricity,24 units of natural gas and 200 units of fuel oil in year 1 using year 1 as the base year?

In testing for whether the median difference of two related populations is zero,the null hypothesis is

SCENARIO 8-17 A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago.His main concern is the total market value of the 3,605 houses in the suburban county.He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample mean market price of $225,000 and a sample standard deviation of $38,700.The consulting group also found out that the mean differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400.Also,the proportion of houses in the sample that are appraised for higher than the market prices is 0.24. -Referring to Scenario 8-17,if he wants a 95% confidence on estimating the true population mean market price of the houses in the suburban county to be within $10,000,how large a sample will he need?

SCENARIO 12-21 A perfume manufacturer is trying to choose between 2 magazine advertising layouts.An expensive layout would include a small package of the perfume.A cheaper layout would include a "scratch- and-sniff" sample of the product.The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate.The manufacturer presents both layouts to 5 groups and determines the approval rating from each group on both layouts.The data are given below.Use this to test whether the median difference in approval rating is different from zero in favor of the more expensive layout with a level of significance of 0.05. -Referring to Scenario 12-21,the hypotheses that should be used are:

SCENARIO 12-20 A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces. -Referring to Scenario 12-20,there is sufficient evidence to conclude that the standard deviation of the amount filled by the machine is not exactly 0.5 ounces when using a 10% level of significance.

SCENARIO 12-19 The director of the MBA program of a state university wanted to know if a one week orientation would change the proportion among potential incoming students who would perceive the program as being good.Given below is the result from 215 students' view of the program before and after the orientation. -Referring to Scenario 12-19,the director should reject the null hypothesis using a 1% level of significance.

To construct a bootstrap confidence interval estimate with confidence level (1- $\alpha$ )100% for the population mean,you will order the resampled means for the m samples that you have drawn from the initial sample of size n,use the value of the resampled mean that cuts off the smallest $\alpha$ 100% as the lower limit and the value of that cuts off the largest $\alpha$ 100% as the upper limit.