BUSINESS QUANTITATIVE ANALYSIS II 6500:222
Sample exam 1 Professor Patankar
Name:___________________________
Instructions: 1. Solve all problems
2. Show all work for full credit
3. 4. 5. Point allocation is indicated in the parentheses. Answers without supporting justification will not receive credit Calculators are permitted.
6. Return the exam and scantron to your instructor when you are finished and before leaving the room
7. Please turn off your cell phones. 8. Please remove your caps.
(6) 1. . On one of the islands the hotel chain had facilities at two different
locations. In tabulating the responses to the single question "Are you likely to choose this hotel again?" 163 out of 227 guests at the Beachcomber responded yes, whereas at the Windsurfer 154 out of 262 guests responded yes. At the = 0.05 level of significance, is there an evidence of a significant difference in guest satisfaction (as measured by likelihood of return to the hotel) between the two hotels?
2
(6) 2. Four secretaries were selected at random from among secretaries of a large
insurance company. The typing speed (words per minute) was recorded for each secretary on an electric typewriter and on a computer keyboard. Secretary Electric Typewriter 74 69 75 64 Computer Keyboard 88 77 79 70
1 2 3 4
Do the data justify the conclusion that the secretaries' typing speeds are greater with a computer keyboard than with an electric typewriter? Use = 0.05. State the hypotheses and explain your conclusions.
3
(5) 3. Maxforce, Inc., manufactures racquetball racquets by two different manufacturing
processes (A and B). Because the management of this company is interested in estimating the difference between the average times it takes each process to produce a racquet, they select independent samples from each process. The results of the samples are shown below. Assume population variances to be 64 and 70 for Process A and Process B respectively.
Process A Sample Size 32 Sample Mean (in minutes) 43
Process B 35 47
Is there conclusive evidence to prove that Process B takes longer than Process A? Use =.05.
4
4. A manufacturing company has four identical machines in a particular production process. Each machine is operated by a different worker. A sample of products produced during a five hour period is taken from each machine and the number of defective parts produced each hour is obtained. One way analysis of variance procedure produced the following analysis of variance table: Source Machines Error Total Degrees of Freedom 3 16 19 SS 300 36 336 MS F ratio
(3) a) Complete the above table. Can you conclude that there is a difference in the average number of defective parts produced by four machines? Use = .01
(4) b) Assume that hourly outputs of defective parts are distributed normally. The average number of defective parts produced per hour are 10, 7, 4 and 6 for machines I, II ,III and IV respectively. Using = 0.01, do machines III and IV produce significantly different number of defective parts?
5
(4) 5. The quality control director for a clothing manufacturer wanted to study the effect of operators and machines on the breaking strength (in pounds) of wool serge material. A batch of material was cut into square yard pieces and these were randomly assigned, three each to all combination of five operators (columns) and three machines (rows) chosen specifically for the experiment. Analysis of variance procedure was performed and following results were obtained. Source of variability Operator Machines Interaction Error Total DF SS 1780 532 810 1557 4679 MS F ratio
Complete the above table.
6
6. A hospital wished administrator to examine post surgical hospitalization periods following knee surgery. A random sample of 30 patients was selected, five for each combination of three age groups and two types of surgery. Two types of surgery: arthroscopy and arthrotomy were used. The age groups selected were under 30, 30 to 50 and over 50 years. The results of the analysis of variance procedure are given below. Source of variability Age Type of surgery Interaction Error Total DF 2 1 2 24 29 SS 3.2 120 1.5 150 MS F ratio
(3) a) Is there a difference in post surgery hospitalization periods between the types of surgery ? Use = .01. State the hypotheses and explain your conclusions.
(3) b) Is there an interaction effect present? Use = .01 Interpret your answer. State the hypotheses and explain your conclusions.
7
(6) 7. Guitars R. US has three stores located in three different areas. Random samples of the sales of the three stores (in $1000) are shown below. Store 1 80 75 76 72 Store 2 85 86 81 88 Store 3 79 85 88 82
Is there a difference in average sales of these three stores? Use = .05.
4 3 2 X ij i 1 j 1
79845
8
(10) 8.Mark the best answer on the scantron 1. If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means a. b. c. d. e. can be approximated by a Poisson distribution will have a variance of one can be approximated by a normal distribution will have a mean of one None of the above answers is correct.
2. An estimate of the variance of a population based on the combination of two sample results is known as the a. pooled standard deviation b. matched variance c. pooled variance estimate d. None of the above answers is correct. 3. The pooled variance is appropriate whenever the two populations a. b. c. d. are normally distributed have equal variances meet both requirements stated in a and b None of the above answers is correct.
4. If we are interested in testing whether the mean of population 1 is smaller than the mean of population 2, the a. b. c. d. e. null hypothesis should state 1 - 2 < 0 null hypothesis should state 1 - 2 > 0 alternative hypothesis should state 1 - 2 < 0 alternative hypothesis should state 1 - 2 = 0 None of the above answers is correct.
5. When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as a. corresponding samples b. matched samples c. independent samples
9
6.In an analysis of variance, one estimate of 2 is based upon the differences between the treatment means and the a. b. c. d. means of each sample overall sample mean sum of observations None of the above answers is correct.
7. The F ratio in a completely randomized ANOVA is the ratio of a. b. c. d. e. MSTR/MSE MST/MSE MSE/MSTR MSE/MST None of the above answers is correct.
8.
The variable of interest in an ANOVA procedure is called a. b. c. d. e. a partition a treatment either a or b a factor None of the above answers is correct.
9. In the ANOVA, treatment refers to a. b. c. d. e. experimental units different levels of a factor a factor applying antibiotic to a wound None of the above answers is correct.
10. An experimental design where the experimental units are randomly assigned to the treatments is known as a. b. c. d. factor block design random factor design completely randomized design None of the above answers is correct.
Answers to the exam 1. Z=3 2. t=3.7
10
3. z=2 4. a) F=44.44 b) LSD=2.77 no difference in machine 3 and 4 5. F(operator) 8.57, F(Machines) 5.13, F(interaction)=1.95 6. a) F=1.92 b) F=.12 7. F=8.53 8. c,c,c,c,b,b,a,d,b,c
11