Exam 22: Binomial Distribution and Normal Approximation

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,what is the standard error of all the sample means?

To construct a bootstrap confidence interval estimate for the population mean,you will first select a random sample of size n with replacement from a population of size N as the initial sample.

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 2 using year 5 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 II 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 is the unweighted aggregate price index for the basket of four food items in 2011 using 2008 as the base year?

SCENARIO 9-11 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 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.05,the probability of making a Type II error is _____ if the mean power consumption of all such microwave ovens is in fact 248 W.

When you use the Poisson distribution to approximate the binomial distribution,the standard deviation is n $\pi$ where n is the sample size and $\pi$ is the probability of an event of interest.

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 smallest $\alpha$ / 2 $\alpha$ 100% as the lower limit and the value of that cuts off the largest $\alpha$ / 2 $\alpha$ 100% as the upper limit.

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

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,what is the probability that the sample mean exceeds the population mean by more than 2 hours?

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 2010 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 12-18 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.She should reject the null hypothesis using a 5% level of significance.

To determine the probability of getting at least 3 events of interest in a binomial distribution,you will find the area under the normal curve for X = 2.5 and above.

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 perfume manufacturer will

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 2010 using 2008 as the base year?

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 2012 that consisted of 40 bushels of wheat,50 bushels of corn,35 bushels of soybeans and 60 hundredweight of milk in 2012 using 2008 as the base year?

SCENARIO 9-11 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 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.01,the probability of making a Type II error is _____ if the mean power consumption of all such microwave ovens is in fact 248 W.

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 0.10,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 2011 that consisted of 60 bushels of wheat,40 bushels of corn,35 bushels of soybeans and 70 hundredweight of milk in 2011 using 2008 as the base year?

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 is the probability that a random sample of 50 will have at least 30% of customers who will make a purchase after visiting the web site?