Exam 22: Binomial Distribution and Normal Approximation

SCENARIO 8-16 A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results. -Referring to Scenario 8-16,of all possible samples of 100 stores taken from the population of 1,000 stores,95% of the confidence intervals developed will contain the true population mean within the interval.

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.What should be her conclusion?

When you use the Poisson distribution to approximate the binomial distribution,the number of events of interest can be larger than the sample size.

Based on past experience,only 0.5% of the invoices of a company contain an error.Out of the 1,500 invoices that the company will issue,what is the approximate probability that no more than 4 invoices will contain an error?

SCENARIO 7-7 Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours.A random sample of 4 students was taken from a population of 50 in order to estimate the mean study time for the population of all students.Use the finite population correction. -Referring to Scenario 7-7,5% of all the samples of 4 will have a sample mean of at least how many hours above the population mean?

SCENARIO 7-8 According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected from a population of 900.Use the finite population correction factor. -Referring to Scenario 7-8,90% of the samples will have more than what percentage of customers who will make a purchase after visiting the web site?

To determine the probability of getting no more than 3 events of interest in a binomial distribution,you will find the area under the normal curve for X = 2.5 and below.

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,what will be the 90% confidence interval for the mean market price of the houses in the suburban county constructed by the consulting group?

The Paasche price index has the disadvantage that current consumption quantities are usually hard to obtain.

SCENARIO 16-16 Given below are the prices of a basket of four food items from 2008 to 2012. -Referring to Scenario 16-16,what is the unweighted aggregate price index for the basket of four food items in 2010 using 2008 as the base year?

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 are the simple price indices for electricity,natural gas and fuel oil,respectively,in year 5 using year 1 as the base year?

SCENARIO 6-7 A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15. -Referring to Scenario 6-7,which of the following is one of the properties required so that the binomial distribution can be used to compute the probability that no more than 2 computers will require repair on a given day?

Practical significance always implies statistical significance.

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,what is the rank of the absolute difference for the last pair of observations?

If a new machine of a production plant is functioning properly,only 1% of the items produced will be defective.Out of the 1,000 items the plant produces on a single day,the approximate probability that at least 0.2% of the items will be defective if the new machine is indeed functioning properly is .

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 unweighted aggregate price index for the group of three energy items in year 4 using year 1 as the base year?

SCENARIO 8-16 A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results. -Referring to Scenario 8-16,if the population had consisted of 1,000 stores,the confidence interval estimate of the mean with finite population correction would have been wider in range.

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,what is the value of the test statistic using a 1% level of significance?

To construct a bootstrap confidence interval estimate for the population mean,you typically select a very large number (in the thousands)of resamples.

When the normality assumption is not met in a randomized block design,which of the following tests should be used?