Exam 22: Binomial Distribution and Normal Approximation

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 2004 for a family that consumed 13 units of electricity,26 units of natural gas and 235 units of fuel oil in year 3 using year 1 as the base year?

One of the reasons that a correction for continuity adjustment is needed when approximating the binomial distribution with a normal distribution is because the probability of getting a specific value of a random variable is zero with the normal distribution.

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 but less than 30 computers that require repair on a given day using a 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,we do not know for sure whether the true population mean is between 5.623 and 6.377 lawnmowers sold.

Bootstrapping makes no assumption about the underlying population distribution.

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 2009 using 2012 as the base year?

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever the sample size is at least 15.

Bootstrapping is used to construct an interval estimate for the population mean when you cannot assume that the population is normally distributed,and the sample size is not large enough to apply the Central Limit Theorem.

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,which pair(s)of observations has a negative signed rank?

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 between 25 and 30 computers that require repair on a given day using a normal approximation.

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 critical value for the 95% one-sided confidence interval for the proportion of students who skipped more than 10 days of school last year?

The Paasche price index is a form of 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 are the simple price indices for electricity,natural gas and fuel oil,respectively,in year 3 using year 5 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,the standard error of all the sample proportions of customers who will make a purchase after visiting the web site is .

For a given level of significance,if the sample size is increased but the summary statistics remain the same,the power of the test will increase.

The Laspeyres price index is a form of weighted aggregate price index.

You use the finite population correction factor when

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 less than what percentage of customers who will make a purchase after visiting the web site?

The Laspeyres price index has the disadvantage that the consumption pattern in the initial period might be quite different from that in the current period and,hence,does not reflect accurately the current consumption cost.

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,what are the lower and upper critical values of the test when allowing for 5% probability of committing a type I error?