Statistical Methods — Summer 2023

Classify each of the following as nominal, ordinal, interval or data. 1. The time required to produce each tire on an assembly line 2. The number of quarts of milk a family drinks in a month 3. The ranking of four machines in your plant after they have been designated as excellent, good, satisfactory, and poor 4. The telephone area code of clients in the United States 5. The age of each of your employees 6. The dollar sales at the local pizza shop each month 7. An employee’s identification number

The owner of a fast-food restaurant ascertains the ages of a sample of customers. From these data, the owner constructs the frequency distribution shown. For each class interval of the frequency distribution, determine the class midpoint, the relative frequency, and the cumulative frequency. Class Interval Frequency 0–under 5 5–under 10 10–under 15 17 15–under 20 23 20–under 25 18 25–under 30 30–under 35 What does the relative frequency tell the fast-food restaurant owner about customer ages?

According to the National Retail Federation and Center for Retailing Education at the University of Florida, the four main sources of inventory shrinkage are employee theft, shoplifting, administrative error, and vendor fraud. The estimated annual dollar amount in shrinkage ($ millions) associated with each of these sources follows: Employee theft $17,918.6 Shoplifting 15,191.9 Administrative error 7,617.6 Vendor fraud 2,553.6 ___________________________ Total $43,281.7 Construct a pie chart and a bar chart to depict these data. Page 1 of

(i) Acompany has 140 employees, of which 30 are supervisors. Eighty of the employees are married, and 20% of the married employees are supervisors. If a company employee is randomly selected, what is the probability that the employee is married and is a supervisor? (ii) Amanufacturing firm produces pads of bound paper. Three percent of all paper pads produced are improperly bound. An inspector randomly samples two pads of paper, one at a time. Because a large number of pads are being produced during the inspection, the sampling being done, in essence, is with replacement. What is the probability that the two pads selected are both improperly bound?

Compute the, mean, median, mode ,variance and standard deviation on the following sample data: Class Interval Frequency Cumulative Frequency 10–under 15 06 15–under 20 22 28 20–under 25 35 63 25–under 30 29 92 30–under 35 16 108 35–under 40 08 116 40–under 45 04 120 45-under 50 02 122

Machines A, B, and Call produce the same two parts, Xand Y. Of all the parts produced, machine Aproduces 60%, machine Bproduces 30%, and machine Cproduces 10%. In addition, 40% of the parts made by machine Aare part X. 50% of the parts made by machine Bare part X. 70% of the parts made by machine Care part X. Apart produced by this company is randomly sampled and is determined to be an Xpart. With the knowledge that it is an Xpart, revise the probabilities that the part came from machine A, B, or C.

Bank customers arrive randomly on weekday afternoons at an average of 3.2 customers every 4 minutes. What is the probability of having more than customers in a 4-minute interval on a weekday afternoon?

What is the probability of obtaining a score greater than 700 on a GMAT test that has a mean of 494 and a standard deviation of 100? Assume GMAT scores are normally distributed. P(X > 700/𝜇 = 540 and 𝜎 = 100) =?

(i) Amanufacturing firm has been involved in statistical quality control for several years. As part of the production process, parts are randomly selected and tested. From the records of these tests, it has been established that a defective part occurs in a pattern that is Poisson distributed on the average of 1.38 defects every 20 minutes during production runs. Use this information to determine the probability that less than 15 minutes will elapse between any two defects. (ii) Suppose that during any hour in a large department store, the average number of shoppers is 448, with a standard deviation of 21 shoppers. What is the probability that a random sample of 49 different shopping hours will yield a sample mean between 441 and 446 shoppers? Page 2 of

Astudy is conducted in a company that employs 800 engineers. Arandom sample of 50 engineers reveals that the average sample age is 34.3 years. Historically, the population standard deviation of the age of the company’s engineers is approximately 8 years. Construct a 98% confidence interval to estimate the average age of all the engineers in this company.

Asurvey of the morning beverage market shows that the primary breakfast beverage for 17% of Americans is milk. Amilk producer in Wisconsin, where milk is plentiful, believes the figure is higher for Wisconsin. To test this idea, she contacts a random sample of 550 Wisconsin residents and asks which primary beverage they consumed for breakfast that day. Suppose 115 replied that milk was the primary beverage. Using a level of significance of .05, test the idea that the milk figure is higher for Wisconsin.

Test the following hypotheses of the difference in population means by using the following data(𝛼 = 0.10) and the eight-step process. H :𝜇 −𝜇 = 0 H :𝜇 −𝜇 < 0 0 1 2 a 1 Sample-1 Sample-2 x = 51.3 x = 53.212 𝜎2 = 52 𝜎2 = 6012 n = 31 n = 3212

Sketch a scatter plot from the following data, and determine the equation of the regression line. x 140 119 103 91 65 29 24 y 25 29 46 70 88 112 128

Test the slope of the regression model developed in Demonstration Problem 12.1 to predict the number of FTEs in a hospital from the number of beds to determine whether there is a significant positive slope. Use a = .01

Compute the coefficient of determination r2 in which a regression model was developed to predict the number of FTEs of a hospital by the number of beds.

Define with example 1. SSE 2. Standard error of estimate 3. Coefficient of Multiple Determination (R2) 4. Adjusted R2

The client company data from the Decision Dilemma reveal that 155 employees worked one of four types of positions. Shown here again is the raw values matrix (also called a contingency table) with the frequency counts for each category and for subtotals and totals containing a breakdown of these employees by type of position and by sex. If an employee of the company is selected randomly, what is the probability that the employee is female or a professional worker? Page 3 of