MATH 533 Final Exam Set 1
1. (TCO A) The number of service calls made in the past 60 days by a sample of 20 technical representatives for AJ TECH is given below.
a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on number of service calls made in the past 60 days.
b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33)
2. (TCO B) Consider the following data on customers at an office supply store. These customers are categorized by their previous volume purchases and their age.
If you choose one customer at random, then find the probability that the customer
a. is a new customer.
b. is a high volume customer and is in the 40′s
c. is in the 20′s, given that the customer is low volume
3. (TCO B) DCW Chemical is planning to implement an acceptance sampling plan for raw materials. A random sample of 22 batches from a large shipment (having a large number of batches) is selected. If two or more of the 22 batches fail to meet specifications, then the entire shipment is returned. Otherwise, the shipment is accepted.
In a sample of 22 batches from a population that is 1% defective (1% of the batches fail to meet specifications), find the probability that
a. two or more batches fail to meet specifications.
b. exactly two batches fail to meet specifications.
c. fewer than two batches fail to meet specifications.
4. (TCO B) CJ Computer Disks stocks and sells recordable CDs. The monthly demand for these CDs is closely approximated by a normal distribution with a mean of 20,000 disks and standard deviation of 4,000 disks. CJ receives shipments from the supplier once per month (at the beginning of each month).
a. Find the probability that the demand for recordable CDs exceeds 30,000 for a particular month.
b. Find the probability that the demand for recordable CDs is between 12,000 and 18,000.
c. How large an inventory must CJ have available at the beginning of the month so that the probability of running out of recordable CDs (a stock out) during the month is no more than .05?
5. (TCO C) A tool manufacturing company wants to estimate the mean number of bolts produced per hour by a specific machine. A simple random sample of 9 hours of performance by this machine is selected and the number of bolts produced each hour is noted. This leads to the following results.
Sample Size = 9
Sample Mean = 62.3 bolts/hr
Sample Standard Deviation = 6.3 bolts/hr
a. Compute the 90% confidence interval for the average number bolts produced per hour.
b. Interpret this interval
c. How many hours of performance by this machine should be selected in order to be 90% confident of being within 1 bolt/hr of the population mean number of bolts per hour by this specific machine?
6. (TCO C) A clock company is concerned about errors in assembly of their custom made clocks. A random sample of 120 clocks from today’s production yields nine clocks with assembly errors.
a. Compute the 95% confidence interval for the percentage of clocks with assembly errors in today’s production
b. Interpret this confidence interval
c. How many clocks should be selected in order to be 95% confident of being within 2% of the population percentage of clocks with assembly errors in today’s production?
7. (TCO D) An article about women in business claims that 28% of all small businesses in the United States are owned by women. Sally Parks believes that this figure is overstated. A random sample of 2,000 small businesses is selected with 546 being owned by women. Does the sample data provide evidence to conclude that less than 28% of small businesses in the United States are owned by women (with a = .10)? Use the hypothesis testing procedure outlined below.
a. Formulate the null and alternative hypotheses
b. State the level of significance
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions
d. Compute the test statistic
e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does the sample data provide evidence to conclude that less than 28% of small businesses in the United States are owned by women (with a = .10)?
8. (TCO D) Bill Smith is the Worthington Township manager. When citizens request a traffic light, the staff assesses the traffic flow at the requested intersection. Township policy requires the installation of a traffic light when an intersection averages more than 150 vehicles per hour. A random sample of 48 vehicle counts is done. The results are as follows:
Sample Size = 48
Sample Mean = 158.3 vehicles/hr.
Sample Standard Deviation = 27.6 vehicles/hr.
Does the sample data provide evidence to conclude that the installation of the traffic light is warranted (using a = .10)? Use the hypothesis testing procedure outlined below.
a. Formulate the null and alternative hypotheses
b. State the level of significance
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions
d. Compute the test statistic
e. Decide whether you can reject Ho and accept Ha or not
f. Explain and interpret your conclusion in part e. What does this mean?
g. Find the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does this sample data provide evidence (with a = 0.10), that the installation of the traffic light is warranted?
MATH 533 Final Exam (Set 2)
1. (TCO A)Seventeen salespeople reported the following number of sales calls completed last month
a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on number of sales calls per month
b. In the context of this situation, interpret the Median, Q1, and Q3
2. (TCO B) Cedar Home Furnishings has collected data on their customers in terms of whether they reside in an urban location or a suburban location, as well as rating the customers as either “good,” “borderline,” or “poor.” The data is below.
If you choose a customer at random, then find the probability that the customer
a. is considered “borderline.”
b. is considered “good” and resides in an urban location
c. is suburban, given that customer is considered “poor.”
3. (TCO B)Historically, 70% of your customers at Rodale Emporium pay for their purchases using credit cards. In a sample of 20 customers, find the probability that
a. exactly 14 customers will pay for their purchases using credit cards
b. at least 10 customers will pay for their purchases using credit cards
c. at most 12 customers will pay for their purchases using credit cards
4. (TCO B) The demand for gasoline at a local service station is normally distributed with a mean of 27,009 gallons per day and a standard deviation of 4,530 gallons per day.
a. Find the probability that the demand for gasoline exceeds 22,000 gallons for a given day
b. Find the probability that the demand for gasoline falls between 20,000 and 23,000 gallons for a given day
c. How many gallons of gasoline should be on hand at the beginning of each day so that we can meet the demand 90% of the time (i.e., the station stands a 10% chance of running out of gasoline for that day)?
5. (TCO C) An operations analyst from an airline company has been asked to develop a fairly accurate estimate of
the mean refueling and baggage handling time at a foreign airport. A random sample of 36 refueling and baggage handling times yields the following results.
Sample Size = 36
Sample Mean = 24.2 minutes
Sample Standard Deviation = 4.2 minutes
a. Compute the 90% confidence interval for the population mean refueling and baggage time
b. Interpret this interval
c. How many refueling and baggage handling times should be sampled so that we may construct a 90% confidence interval with a sampling error of .5 minutes for the population mean refueling and baggage time?
6. (TCO C) The manufacturer of a certain brand of toothpaste claims that a high percentage of dentists recommend the use of their toothpaste. A random sample of 400 dentists results in 310 recommending their toothpaste.
a. Compute the 99% confidence interval for the population proportion of dentists who recommend the use of this toothpaste.
b. Interpret this confidence interval
c. How large a sample size will need to be selected if we wish to have a 99% confidence interval that is accurate to within 3%?
7. (TCO D) A Ford Motor Company quality improvement team believes that its recently implemented defect reduction program has reduced the proportion of paint defects. Prior to the implementation of the program, the proportion of paint defects was .03 and had been stationary for the past 6 months. Ford selects a random sample of 2,000 cars built after the implementation of the defect reduction program. There were 45 cars with paint defects in that sample. Does the sample data provide evidence to conclude that the proportion of paint defects is now less than .03 (with = .01)? Use the hypothesis testing procedure outlined below.
a. Formulate the null and alternative hypotheses
b. State the level of significance
c. Find the critical value (or values), and clearly show the rejection and non-rejection regions
d. Compute the test statistic
e. Decide whether you can reject Ho and accept Ha or not
f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does the sample data provide evidence to conclude that the proportion of paint defects is now less than .03 (with = .01)?
8. (TCO D) A new car dealer calculates that the dealership must average more than 4.5% profit on sales of new cars. A random sample of 81 cars gives the following result.
Sample Size = 81
Sample Mean = 4.97%
Sample Standard Deviation = 1.8%
Does the sample data provide evidence to conclude that the dealership averages more than 4.5% profit on sales of new cars (using = .10)? Use the hypothesis testing procedure outlined below.
a. Formulate the null and alternative hypotheses
b. State the level of significance
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions
d. Compute the test statistic
e. Decide whether you can reject Ho and accept Ha or not
f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does the sample data provide evidence to conclude that the dealership averages more than 4.5% profit on sales of new cars (using = .10)?
9. (TCO E) Bill McFarland is a real estate broker who specializes in selling farmland in a large western state. Because Bill advises many of his clients about pricing their land, he is interested in developing a pricing formula of some type. He feels he could increase his business significantly if he could accurately determine the value of a farmer’s land. A geologist tells Bill that the soil and rock characteristics in most of the area that Bill sells do not vary much. Thus the price of land should depend greatly on acreage. Bill selects a sample of 30 plots recently sold. The data is found below (in Minitab), where X=Acreage and Y=Price ($1,000s).
a. Analyze the above output to determine the regression equation
b. Find and interpret in the context of this problem.
c. Find and interpret the coefficient of determination (r-squared).
d. Find and interpret coefficient of correlation
e. Does the data provide significant evidence (= .05) that the acreage can be used to predict the price? Test the utility of this model using a two-tailed test. Find the observed p-value and interpret
f. Find the 95% confidence interval for mean price of plots of farmland that are 50 acres. Interpret this interval
g. Find the 95% prediction interval for the price of a single plot of farmland that is 50 acres. Interpret this interval
h. What can we say about the price for a plot of farmland that is 250 acres?
10. (TCO E)An insurance firm wishes to study the relationship between driving experience (X1, in years), number of driving violations in the past three years (X2), and current monthly auto insurance premium (Y). A sample of 12 insured drivers is selected at random. The data is given below (in MINITAB):
a. Analyze the above output to determine the multiple regression equation
b. Find and interpret the multiple index of determination (R-Sq).
c. Perform the t-tests on and on (use two tailed test with (= .05). Interpret your results
d. Predict the monthly premium for an individual having 8 years of driving experience and 1 driving violation during the past 3 years. Use both a point estimate and the appropriate interval estimate
MATH 533 Final Exam SET 3
1. (TCO A)Consider the following raw data, which is the result of selecting a random sample of 20 Bank Common Stocks and noting the dividend yields (as a %).
2. (TCO B) The general manager of Oak Place Mall has collected data on where each customer lives and the gender of each customer. A random sample of 500 customers was selected with the results below.
3. (TCO B)In a recent survey, 80% of the citizenry in a community favored the building of a municipal golf course. If you ask 15 citizens about this project, find the probability that
4. (TCO B) A study of homeowners in the 5th congressional district in Maryland found that their annual household incomes are normally distributed with a mean of $41,182 and a standard deviation of $11,990 (based on data from Nielsen Media Research).
5. (TCO C) Until this year, the mean braking distance of a Nikton automobile moving at 60 mi per hour was 175 ft. Nikton engineers have developed what they consider a better braking system. They test the new brake system on a random sample of 81 cars and determine the sample mean braking distance. The results are the following
6. (TCO C) You are in charge of selling advertising for radio station WQAA. The fee you can set for airtime is directly related to the share of the listening market your station reaches. From time to time, you conduct surveys to determine WQAA’s share of the market. This month, when you contacted 200 randomly selected residential phone numbers, 12 respondents said they listen to WQAA
7. (TCO D) Persons living near a smelting plant have complained that the plant violates the city’s noise pollution code. The code states that to be in compliance, noise levels are only allowed to exceed 120 decibels less than 10% of the time. You monitor the noise levels at 150 randomly selected times and found that 11 were above 120 decibels. Does the sample data provide evidence to conclude that the plant is in compliance with the noise pollution code (witha = .05)? Use the hypothesis testing procedure outlined below.
8. (TCO D)Bill Smith is the Worthington Township manager. When citizens request a traffic light, the staff assesses the traffic flow at the requested intersection. Township policy requires the installation of a traffic light when an intersection averages more than 150 vehicles per hour. A random sample of 48 vehicle counts is done. The results are as follows:
(TCO E) Management at New England Life wants to establish the relationship between the number of sales calls made each week (CALLS, X) and the number of sales made each week (SALES, Y). A random sample of 18 life insurance salespeople were surveyed yielding the data found below
(TCO E) A local realtor wishes to study the relationship between selling price (PRICE in $), house size (HOUSESIZE in square feet), lot size (LOTSIZE in acres), and number of bathrooms (BATHROOM). A sample of 10 homes is selected at random. The data is given below (in MINITAB)
