Exam 22: Binomial Distribution and Normal Approximation

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 population proportion of houses that will be appraised for higher than the market prices?

Statistical significance does not necessarily imply practical significance.

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 drawn from the population of 1,000 stores,95% of the sample means will fall between 5.623 and 6.377 lawnmowers.

SCENARIO 8-12 The superintendent of a unified school district of a small town wants to make sure that no more than 5% of the students skip more than 10 days of school in a year.A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year. -Referring to Scenario 8-12,what is the upper bound of the 95% one-sided confidence interval for the proportion of students who skipped more than 10 days of school last 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 is the Laspeyres price index for the group of three energy items in year 5 for a family that consumed 15 units of electricity,24 units of natural gas and 200 units of fuel oil in year 1 using hear 1 as the base year?

The more expensive commodities are overly influential in an unweighted aggregate price index.

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 Paasche price index for the group of three energy items in year 4 for a family that consumed 13 units of electricity,26 units of natural gas and 235 units of fuel oil in year 4 using year 1 as the base year?

SCENARIO 9-12 A drug company is considering marketing a new local anesthetic.The effective time of the anesthetic the drug company is currently producing has a normal distribution with a mean of 7.4 minutes with a standard deviation of 1.2 minutes.The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic. -Referring to Scenario 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.1,the probability of a Type I error is _____ if the population mean effective time is 8 minutes.

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 are the simple price indices for wheat,corn,soybeans and milk,respectively,in 2012 using 2008 as the base year?

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 at least 4 invoices will contain an error?

SCENARIO 8-13 The president of a university is concerned that illicit drug use on campus is higher than the 5% targeted level.A random sample of 250 students from a population of 2,000 revealed that 7 of them had used illicit drugs during the last 12 months. -Referring to Scenario 8-13,what is the upper bound of the 90% one-sided confidence interval for the proportion of students who had used illicit drugs during the last 12 months?

SCENARIO 9-12 A drug company is considering marketing a new local anesthetic.The effective time of the anesthetic the drug company is currently producing has a normal distribution with a mean of 7.4 minutes with a standard deviation of 1.2 minutes.The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic. -Referring to Scenario 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.1,the confidence coefficient of the test is _____ if the population mean effective time is 8 minutes.

SCENARIO 9-14 An appliance manufacturer claims to have developed a compact microwave oven that consumes a population mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim. -Referring to Scenario 9-14,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.05,the power of the test is _____ if the mean power consumption of all such microwave ovens is in fact 257.3 W.

To determine the probability of getting between 2 and 4 events of interest in a binomial distribution,you will find the area under the normal curve between X = 1.5 and 4.5.

The director of a training program wanted to know if a one week orientation would change the perception of potential clients who would perceive the program as being good.He collected information on the number of clients who would rate the program as being good before and after the orientation.Which of the following tests will be the most appropriate?

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 exactly 0.2% of the items will be defective if the new machine is indeed functioning properly is .

When using the normal approximation to the binomial distribution,which of the following is the correct range of x for finding the probability of getting 3 through 6 heads when tossing a coin 10 times?

In measuring the effect size of the difference between two population means,the rule of thumb suggests that a standardized effect size of around 0.8 can be classified as large.

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 is the p-value of the test statistic using a 5% level of significance?

The McNemar test is used to determine whether there is evidence of a difference between the proportions of two related samples.