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 7-7,10% of all the samples of size 4 will have a sample mean of at least how many hours below the population mean?

SCENARIO 8-14 The president of a university is concerned that the percentage of students who have cheated on an exam is higher than the 1% acceptable level.A confidential random sample of 1,000 students from a population of 7,000 revealed that 6 of them said that they had cheated on an exam during the last semester. -Referring to Scenario 8-14,what is the upper bound of the 90% one-sided confidence interval for the proportion of students who had cheated on an exam during the last 12 months?

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 400 stores,the confidence interval estimate of the mean with finite population correction would have been wider in range.

The base period for a simple price index should be recent so that a price index is not severely affected by change in technology,and consumer attitudes and habits.

SCENARIO 9-13 A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience,the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours. -Referring to Scenario 9-13,if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.10,the power of the test is _____ if the population mean bulb life is 490 hours.

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?

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,there is sufficient evidence to conclude that the standard deviation of the amount filled by the machine is not exactly 0.5 ounces when using a 5% level of significance.

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,the president can be 90% confident that no more than 5% of the students at the university had used illicit drugs during the last 12 months.

The number of resamples is irrelevant in constructing a bootstrap confidence interval estimate for the population mean.

The consumer price index is a Paasche price index.

In measuring the effect size of the difference between two population means,the rule of thumb suggests that a standardized effect size of around 0.2 can be classified as large.

To test whether one proportion is higher than the other in two related samples,you can use the Marascuilo procedure.

To construct a bootstrap confidence interval estimate for the population mean,you will resample the initial sample of size n by selecting n values without replacement from the n values in the initial sample for m different times.

The finite population correction factor is

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever n $\pi$ is at least 5.

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 5 using year 1 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 0.10,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 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 4 using year 1 as the base year?

Which of the following is not true regarding sampling in auditing?

SCENARIO 8-14 The president of a university is concerned that the percentage of students who have cheated on an exam is higher than the 1% acceptable level.A confidential random sample of 1,000 students from a population of 7,000 revealed that 6 of them said that they had cheated on an exam during the last semester. -Referring to Scenario 8-14,the president can be 90% confident that no more than 1% of the students at the university had cheated on an exam during the last semester.