Exam 22: Binomial Distribution and Normal Approximation

The bootstrap confidence interval estimate for the population mean is constructed based on the sampling distribution of the m population means.

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,what proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the web site?

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 and assuming that the number of computers that requires repair on a given day follows a binomial distribution,compute the probability that there will be exactly 10 computers that require repair on a given day using a normal approximation.

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 null hypothesis should be rejected.

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 critical value for the 90% one-sided confidence interval for the proportion of students who had used illicit drugs during the last 12 months?

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,the p-value of the test is somewhere between 5% and 10%.

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 2012 using 2008 as the base year?

SCENARIO 9-15 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 9-15,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.01,the probability of the company marketing the new local anesthetic when its population mean effective time is greater than the 7.4 minutes is _____ if the population mean effective time is 8 minutes.

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 and assuming that the number of computers that requires repair on a given day follows a binomial distribution,compute the probability that there will be more than 25 computers that require repair on a given day using a normal approximation.

To construct bootstrap confidence interval estimate for the population mean with confidence level (1- $\alpha$ )100% ,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 largest $\alpha$ / 2 $\alpha$ 100% as the lower limit and the value of that cuts off the smallest $\alpha$ / 2 $\alpha$ 100% as the upper limit.

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 less than 4 invoices will contain an error?

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 Laspeyres price index for the basket of four food items in 2012 that consisted of 50 bushels of wheat,30 bushels of corn,40 bushels of soybeans and 80 hundredweight of milk in 2008 using 2008 as the base year?

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 12-18,what type of test should be performed?

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 0.01,the probability of the company incorrectly marketing the new local anesthetic when its population mean effective time is not greater than the 7.4 minutes is .

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 0.01,the probability of the company failing to market the new local anesthetic when its population mean effective time is greater than the 7.4 minutes 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 248 W.

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 Paasche price index for the basket of four food items in 2010 that consisted of 50 bushels of wheat,30 bushels of corn,40 bushels of soybeans and 80 hundredweight of milk in 2010 using 2008 as the base year?

A researcher is curious about the effect of sleep on students' test performances.He chooses 60 students and gives each 2 tests: one given after 2 hours' sleep and one after 8 hours' sleep.The test the researcher should use would be a related samples test.

To determine the probability of getting more than 3 events of interest in a binomial distribution,you will find the area under the normal curve for X = 3.5 and above.

To construct a bootstrap confidence interval estimate for the population mean,you do not need a very large number (in the thousands)of resamples.