Question 1- The employee benefits manager of a medium size business would like to estimate the proportion of full-time employees who prefer adopting plan A of three available health care plans in the coming annual enrollment period. A reliable frame of the company's employees and their tentative health care preferences are available. Using Excel, the manager chose a random sample of size 50 from the frame. There were 17 employees in the sample who preferred plan A.
What is the upper limit of a 99% confidence interval for the proportion of company employees who prefer plan A. Assume that the population consists of the preferences of all employees in the frame.
Question 2- Lilliefors test for normality compare two cumulative distribution functions (cdf's): the cdf from a normal distribution and the cdf corresponding to the given data (called the empirical cdf).
True
False
Question 3- The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold.
What is the probability that at least one of the 20 new microwaves sold will require a warranty repair in the first 90 days?
Question 4- Suppose a firm that produces light bulbs wants to know whether it can say that its light bulbs typically last more than 1500 hours. Hoping to find support for their claim, the firm collects a random sample and records the lifetime (in hours) of each bulb. The information related to the hypothesis test is presented below.
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Test of Mean
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Hypothesized mean
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1500.0
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Sample mean
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1509.5
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Std error of mean
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4.854
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Degrees of freedom
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24
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t-test statistic
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1.953
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p-value
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0.031
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The sample size can be determined from the information above. Therefore the sample size n = Blank 1. The sample mean of this data is Blank 2. If you use a 5% significance level, would you conclude that the mean life of the light bulbs is typically more than 1500 hours? Yes or no Blank 3.
If you were to use a 1% significance level in this case, would you conclude that the mean life of the light bulbs is typically more than 1500 hours? Yes or no Blank 4.
Question 5- In general, the paired-sample procedure is appropriate when the samples are naturally paired in some way and there is a reasonably large positive correlation between the pairs. In this case, the paired-sample procedure makes more efficient use of the data and generally results in narrower confidence intervals.
True
False
Question 6- A department store in a small town is in the process of budget planning and will be building a decision tree to select the best option among its available marketing channels. To estimate the probabilities it will need, it considers a customer base of 1500 individuals, 700 of which are women. Data shows that 240 of the women in this population earn at least $50,000 per year and 300 of the men earn at least $50,000 per year.
If a randomly selected individual is observed to earn less than $50,000 per year, what is the probability that this person is a woman? (No approximations, at least 4 decimal digits).
Question 7- A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not approve the loan application, the $20,000 will be invested in bonds that earn a 6% annual return. Without additional information, the credit union believes that there is a 5% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the credit union will lose the $20,000.
What is the credit union maximum expected profit?
Question 8- Senior management of a consulting services firm is concerned about a growing decline in the firm's weekly number of billable hours. The firm expects each professional employee to spend at least 40 hours per week on work. In an effort to understand this problem better, management would like to estimate the standard deviation of the number of hours their employees spend on work-related activities in a typical week. Rather than reviewing the records of all the firm's full-time employees, the management randomly selected a sample of size 50 from the available frame. The sample mean and sample standard deviations were 48.5 and 7.5 hours, respectively. They can state that "We are 99% confident that the population standard deviation is between Blank 1 and Blank 2.
Question 9- A 90% confidence interval estimate for a population mean is determined to be 72.8 to 79.6. If the confidence level is reduced to 80%, the confidence interval for becomes narrower.
True
False
Question 10- Auditors of Independent Bank are interested in comparing the reported value of all 1775 customer savings account balances with their own findings regarding the actual value of such assets. Rather than reviewing the records of each savings account at the bank, the auditors randomly selected a sample of 100 savings account balances from the frame. The sample mean and sample standard deviations were $505.75 and 360.95, respectively. Auditors may state that "We are 90% confident that the total balance of all 1775 savings account balances within the bank is approximately between Blank 1 and Blank 2.
Question 12- A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decide in November how many footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Furthermore, assume that each pair can be sold for a retail price of $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footballs (in hundreds) during the upcoming season has been assessed by the market research specialists and is presented below. Finally, assume that the sporting goods store chain must purchase the footballs in lots of 100 units.
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Demand (in hundreds)
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Probability
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4
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0.30
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5
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0.50
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6
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0.20
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What is the expected profit in the optimal strategy case?
Question 13- If the sample size is greater than 30, the Central Limit Theorem (CLT) will always apply.
True
False
Question 14- The owner of a radio station in a rapidly growing community in central Texas is about to begin operations and must decide what type of program format to offer. She is considering three formats; rock, country, and rap. The number of listeners for a particular format will depend on the type of potential audience that is available. Income from advertising depends on the number of listeners the station has. Three broad categories of audience type can be described as A1, A2, and A3. The rock music format draws mainly for the A1 listener, the country music format draws mainly from the A2 listener and the rap music format draws mainly from the A3 listener. The station owner does not know which type of audience will dominate the community once its growth has stabilized. Probabilities have been assigned to the potential dominant audience, based on the community growth that has already occurred in this area. Since she wants to begin building an image now, the decision as to which format to adopt must be made in an environment of uncertainty. The station owner has been able to construct the following payoff table, in which the entries are average monthly revenue in thousands of dollars.
Audience
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Format
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A1
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A2
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A3
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Rock
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$ 110
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$ 80
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$ 70
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|
Country
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$ 90
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$ 120
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$ 50
|
|
Rap
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$ 70
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$ 60
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$ 140
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Probability
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0.3
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0.5
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0.2
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What is the expected profit in that case?
Question 15- We can form a confidence interval for the population total T by finding a confidence interval for the population mean in the usual way, and then multiplying the lower and upper limits the confidence interval by the population size N.
True
False
Question 16- The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold.
What is the standard deviation of the number of the new microwaves sold that will require a warranty repair in the first 90 days?
Question 17- A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decide in November how many footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Furthermore, assume that each pair can be sold for a retail price of $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footballs during the upcoming season has been assessed by the market research specialists and is presented below. Finally, assume that the sporting goods store chain must purchase the footballs in lots of 100 units.
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Demand
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Probability
|
|
400
|
0.30
|
|
500
|
0.50
|
|
600
|
0.20
|
What is the optimal strategy for order quantity? (
Question 18- Q-Mart is interested in comparing customer who used its own charge card with those who use other types of credit cards. Q-Mart would like to know if customers who use the Q-Mart card spend more money per visit, on average, than customers who use some other type of credit card. They have collected information on a random sample of 38 charge customers as shown below. On average, the person using a Q-Mart card spends $192.81 per visit and customers using another type of card spend $104.47 per visit.
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Summary statistics for two samples
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Q-Mart
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Other Charges
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Sample sizes
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13
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25
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Sample means
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192.81
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104.47
|
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Sample standard deviations
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115.243
|
71.139
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Confidence interval for difference between means
|
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Sample mean difference
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88.34
|
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Pooled standard deviation
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88.323
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Std error of difference
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30.201
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Using a t - value of 2.0281, the lower limit of a 95% confidence interval for the difference between the average Q-Mart charge and the average charge on another type of credit card is Blank 1.
Question 19- Cluster sampling is often less convenient and more costly than other random sampling methods.
True
False
Question 20- A battery manufacturer wants to estimate the average number of defective (or dead) batteries contained in a box shipped by the company. Production personnel at this company have recorded the number of defective batteries found in each of the 2000 boxes shipped in the past week.
What sample size would be required for the production personnel to be approximately 95% sure that their estimate of the average number of defective batteries per box is within 0.3 unit of the true mean? Assume that the best estimate of the population standard deviation is 0.9 defective batteries per box.