Mgtsc312_F2023_Midterm1_Soln_21Oct2023

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University of Alberta *

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312

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Statistics

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Apr 3, 2024

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Simulating a random value from the Chi-Square distribution with df= =CHISQ.INV.RT(RAND(),9) 5.003384364 11.03778449 Parts Points ID 2 Rand 3 Q1 to Q5 11 Q6 to Q10 14 Q11 to Q12 7 Q13 to Q15 9 Q16 to Q19 13 Q20 to Q24 8 Q25 to Q30 14 Q31 to Q34 11 Q35 to Q37 10 Q38 3 105 [3 pts.] Rand: Propagate the formula from the Answer worksheet [ paste as values 1 Completing this section is crucial; failing t grade. Note: This exercise has been there in all pr hand, and a TA will help you to complete Good Luck!
=9 m B3 to B4. Copy the value from B4 as Paste Special in cell C5 of 123 ] - do not copy the formula to the Answer sheet to do so will result in a 10% deduction from your Midterm 1 final revious lab assignments. If you have a question, you can raise your e this part .
Please do not delete any cells/columns/rows in this worksheet. Total points in t worksheet: 11 The following applies to the next five questions – 11 points Comparing Phones. Table 1 shows data for eight phones (Consumer Reports). The Overall Sco the overall quality of the phone, ranges from 0 to 100. Voice Quality has possible ratings of poor good, and excellent. Talk Time is the manufacturer’s claim of how long the phone can be used charged. Numerical answers for questions 3, 4, 5: you can calculate anywhere (or directly) designated cells of V5, V6 and V7 respectively (or directly in the designated cells). [2 pts.] The number of entities in this dataset [ MC : select from the drop-down menu] is: 4 6 8 32 None of the above [2 pts.] The number of categorical variables in this dataset [ MC : select from the drop-down me 1 2 3 4 None of the above [2.5 pts.] What is the median Overall Score for the phones? [2.5 pts.] What is the average Talk Time for the phones? [2 pts.] What percentage of the phones have a Voice Quality of Excellent ?
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Table 1: Q1 - Q5 Model Brand Price ($) CL84100 AT&T 60 73 Excellent 7 TL92271 AT&T 80 70 Good 7 4773B 110 78 13 6592T 70 72 13 D2997 Uniden 45 70 Good 10 D1788 Uniden 80 73 7 DS6521 Vtech 60 72 Excellent 7 CS6649 Vtech 50 72 7 Questions from Chapters 1 - 3 Q3-5: calculations are done in Lab Cycle 1 Overall Score Voice Quality Talk Time (hours) Panasoni c Very Good Panasoni c Very Good Very Good Very Good this ore, a measure of r, fair, good, very d when it is fully and place in the enu] is:
Questions Answers 1 c. 2 a. Some might consider 'Brand' as another categorical variable with repeated ob 3 72 4 8.875 12 5 9.142857143
bservations per brand
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Please do not delete any cells/columns/rows in this worksheet. Total points in The following applies to the next five questions – 14 points Days Listed Until Sold.  Cooper Realty is a small real estate company located in Albany, New in residential listings. They recently became interested in determining the likelihood of one within a certain number of days. An analysis of company sales of 800 homes in previous years ( Table 2 ): [2.5 pts.] What is the probability that a randomly selected house was listed with an initial $199,999? [2.5 pts.] What is the probability that a randomly selected house was listed for 31 – 90 days w $200,000 – $250,000 ? [3 pts.] What is the probability that a randomly selected house had an initial asking price of at [3 pts.] What is the probability that a randomly selected house will be sold in under 30 days an initial asking price of $150,000 – $199,999 ? [3 pts.] Define A as the event indicating selling under 30 days. Define B as the event wit $150,000 – $199,999. Based on the details given on the Initial Asking Price and Days List following statements is correct? [ MC: select from the drop-down menu] Initial Asking Price and Days Listed Until Sold are independent as P(A│B)=P(A) Initial Asking Price and Days Listed Until Sold are independent as P(A│B)=P(B) Initial Asking Price and Days Listed Until Sold are not independent as P(A│B)≠P(A) Initial Asking Price and Days Listed Until Sold are not independent as P(A│B)≠P(B) Not enough information to comment Questions 6, 7, 8, 9 numerical answers only : you can calculate anywhere (or directly) and p V3, V4, V5 and V6 respectively
Table 2: Q6 - Q10 Days Listed Until Sold 31–90 Over 90 Total 50 40 10 100 20 150 80 250 20 280 100 400 10 30 10 50 Total 100 500 200 800 Questions from Chapter 4 Under 30 Initial Asking Price Under $150,000 $150,000– $199,999 $200,000– $250,000 Over $250,000 Q5-10: calculations are done in Lab Cycle 2 and concepts are co Lecture 2 (slides 14 - 20) and lab-cycle 2 example on Pivot applications, based on suggested problem 14.56 this worksheet: 14 York, specializing primarily e of their listings being sold produced the following data asking price of $150,000 – with an initial asking price of least $200,000 ? given that it was listed with th an initial asking price of ted until Sold, which of the place in the designated cells:
Questions Answers 6 0.3125 7 0.35 8 0.5625 9 0.08 10 c. overed in Table
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Please do not delete any cells/columns/rows in this worksheet. Total points i worksheet: 16+13 = 29 The following applies to the next two questions – 7 points Introductory Statistics Course Withdrawals . A university found that 15% of its students completing the introductory statistics course. Assume that 20 students registered for the cours [3 pts.] What is the probability that none of the students will withdraw? [4 pts.] What is the probability that more than one student will withdraw?   The following applies to the next three questions – 9 points U.S. Unemployment.  A Newspaper reported that the average number of weeks an individu is 17.5 weeks. Assume that for the population of all unemployed individuals, the populatio unemployment is 17.5 weeks; and that the population standard deviation is four week unemployment duration follows a Normal distribution. Suppose you would like to selec unemployed individuals for a follow-up study. [3 pts.] What is the probability that a randomly selected individual will remain unemployed weeks? [2 pts.] What is the standard error of the sample mean length of unemployment? [4 pts.] What is the probability that a simple random sample of 50 unemployed individua sample mean within one week of the population mean? Questions 11 to 15 numerical answers only : you can calculate anywhere (or directly) and p designated cells: V3 to V7 respectively
Q11 - 12 from Chapter 5: concepts covered in Lecture 2, slides 29 - 31, similar problems on Binomial Distribution Q13 - 15 from Chapters 6 and 7: concepts covered in Lecture 2, slides 39-51, a slides 8-11, similar to suggested problems on Normal Distribution for X a Q16 - 19 from Chapters 5 and 6: concepts covered in Lecture 2, slides 32-33, 5 example was done in the lecture on slides 57-58) in this withdraw without se. ual is unemployed on mean length of ks. Also, assume t a sample of 50 d for more than 20 als will provide a place in the Please do not delete any cells/columns/rows in this worksheet. The following applies to the next four questions – 13 points Heavy Trucks . You are responsible for planning logistical support for heavy trucks operating in Fort McMurray. The time between breakdowns follows an Exponential distribution with a mean of 2.5 days [4 pts.] What is the probability that it takes more than 3.25 days between the next two breakdowns? Since you have to buy parts for two-week periods (i.e. a fortnight), you are interested in the distribution of the number of breakdowns (X) per fortnight (that is, 2 weeks). [2 pts.] What is the mean number of breakdowns per fortnight? (Do not round) [3 pts.] What is the probability of getting exactly two breakdown in the next fortnight? [4 pts.] What is the probability of getting three or more breakdowns in the next fortnight? Questions 17 to 19 numerical answers only : you can calculate anywhere (or directly) and place in the designated cells: V8 to V11 respectively
Questions Answers 11 0.038759531 12 0.824442124 13 0.265985529 14 0.565685425 15 0.922900128 16 0.272531793 17 5.6 18 0.057982503 0.057983 19 0.917611596 Z-score -1.76776695 15_Using Table 0.923 0.9232 r to suggested and Lecture 3, and X-bar 52-58 (similar
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Please do not delete any cells/columns/rows in this worksheet. The following applies to the next five questions – 8 points Weekly Sales Reports.  Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 25 weekly reports showed a sample mean of 19.5 customer contacts per week. Suppose the population standard deviation was known to be 5.2. Assume the number of customer contacts follows a Normal Distribution. Construct an 80% confidence interval (CI) for the population mean number of weekly customer contacts for the sales personnel by answering the following questions. [1 pt.] What is the point estimate of the population mean number of weekly customer contacts for the sales personnel? [2 pts.] What is the standard error of the sample mean number of weekly customer contacts for the sales personnel? [2 pts.] What is the critical value on the upper tail for developing an 80% CI for the population mean number of weekly customer contacts for the sales personnel given the details provided here? [1.5 pts.] What is the MOE for the above-stated 80% CI? [1.5 pts.] What is the upper limit of the 80% CI for the population mean number of weekly customer contacts for the sales personnel? Please do not delete any c The following applies to th Attitudes toward Superm as good as national name asked a sample of 100 shop stated that the supermarket [2 pts.] The null and altern drop-down menu] H_0: P ̅=0.65 vs. H_a: P ̅≠0 H_0: X ̅=65 vs. H_a: X ̅≠65 H_0: P=0.65 vs. H_a: P≠0.6 H_0: μ=65 vs. H_a: μ≠65 Not enough information to [2 pts.] The sample size req Min(np ̅, n(1−p ̅ ))≥5 Min(np_o, n(1−p_o ))≥5 n>=30 n>=50 None of the above conditio [2.5 pts.] What is the stand [2.5 pts.] What is the test s [3 pts.] What is the p-value [2 pts.] Based on the p-val 𝛼=1% ; what is your conclu We do not have enough inf We have enough informatio We do not have enough evi We have enough evidence t None of the above is correc Questions 20 to 24 and 27 to 28 numerical answers only : you can calculate anywhere (or directly) and place in the designated cells: V3 to V7 and V10 to V12 respectively. Q30 is MC with 5 options (scroll down to see the complete question)
cells/columns/rows in this worksheet. Total points in this worksheet: 8+14 = 22 he next six questions – 14 points market Brands . A study by  Consumer Reports  showed that 65% of supermarket shoppers believe superm brands. To investigate whether this result applies to its own product, the manufacturer of a national n ppers whether they believed that supermarket ketchup was as good as the national brand ketchup. Amon t brand was as good as the national brand native hypotheses to test that supermarket ketchup was as good as the national brand ketchup are: [ M 0.65 5 65 formulate the hypotheses  quirement for the Supermarket Brands scenario is: [ MC: select from the drop-down menu] ons is correct dard error of the point estimate of shoppers who stated that the supermarket brand was as good as the na statistic value to test that supermarket ketchup was as good as the national brand ketchup? e to test that supermarket ketchup was as good as the national brand ketchup? lue you obtained in the previous question to test that supermarket ketchup was as good as the national b usion? [ MC: select from the drop-down menu] formation to reject the null hypothesis that supermarket ketchup was as good as the national brand ketchu on to reject the null hypothesis that supermarket ketchup was as good as the national brand ketchup idence to reject the null hypothesis that supermarket ketchup was as good as the national brand ketchup. to reject the null hypothesis that supermarket ketchup was as good as the national brand ketchup. ct
Questions Answers 20 19.5 21 1.04 22 1.2815515655 23 1.3328136282 24 20.832813628 25 c. 26 b. 27 0.0476969601 28 -2.096569673 29 0.0360316862 30 c. Q20 - 24 from Chapter 8: concepts covered in Lecture 3, slides 25 (all requ have been done both during lecture and lab-cycle 2) Q25 - 30 from Chapter 9: concepts covered in Lecture 3, slides 53-56 (all re have been done both during lecture and lab-cycle 2) market brands to be name-brand ketchup ng 100 shoppers 55 MC: select from the ational brand? brand ketchup, with up
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uired calculations equired calculations
Please do not delete any cells/columns/rows in this worksheet. Total points in this worksh The following applies to the next four questions – 11 points PGA Tour Scores.  Scores in the first and fourth (final) rounds for a sample of 15 randomly s competed in PGA tournaments are shown in the following table. Suppose you would like to de score for the first round of a PGA Tour event is significantly different from the mean score for round. Assume Golf Scores follow a Normal Distribution. Table 3 contains the related data. Suppose you want to test for a statistically significant difference between two population the above-stated test, complete the following parts: Hint. You can use either Excel functions, e.g., Average, VAR.S, etc., or Data Analysis T relevant summary statistics for any sample data [2.5 pts.] What is the point estimate of the difference between the two population means? [3 pts.] What is the standard error of the point estimate of the difference between the two pop [2.5 pts.] What is the Test Statistic to test for a statistically significant difference betw means? [3 pts.] What is the p-value to test for a statistically significant difference between two popu Questions 31 and 34 numerical answers only : you can calculate anywhere and place in the de to V4 respectively.
Table 3: Q31 - Q34 Player Round 1 Round 2 Difference Michael Letzig 70 72 -2 Scott Verplank 71 72 -1 D.A. Points 70 75 -5 Jerry Kelly 72 71 1 Soren Hansen 70 69 1 D.J. Trahan 67 67 0 Bubba Watson 71 67 4 Reteif Goosen 68 75 -7 Jeff Klauk 67 73 -6 Kenny Perry 70 69 1 Aron Price 72 72 0 Charles Howell 72 70 2 Jason Dufner 70 73 -3 Mike Weir 70 77 -7 Carl Patterson 68 70 -2 Q31 - 34 from Chapter 10: concepts covered in Lecture 4, slides 16-2 for a very similar example 10.21 were done in heet: 11 selected golfers who etermine if the mean r the fourth and final means. To complete Toolpak to calculate pulation means? ween two population ulation means? esignated cells: V3
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Questions Answers 31 -1.600 32 0.877225062 33 -1.8239333 34 0.089576741 -1.600 21 (Additionally, calculations n class)
Q35 - 3 Q38 Please do not delete any cells/columns/rows in this worksheet. Total points in this worksheet: 10+3 = 13 The following applies to the next three questions – 10 points Volatility of General Electric Stock.  To analyze the risk, or volatility, associated with investing in General Electric common stock, consider a sample of the eight quarterly percent total returns. The percent total return includes the stock price change plus the dividend payment for the quarter. Assume returns follow a Normal distribution. Table 4 contains the related data. Hint. You can use either Excel functions, e.g., Average, VAR.S, STDEV.S, etc., or Data Analysis Toolpak to calculate relevant summary statistics for any sample data [3 pts.] Calculate the sample variance and standard deviation as measures of volatility for the quarterly return for General Electric. [3 pts.] Suppose you want to construct a 95% confidence interval for the population variance . What is the upper limit (UL) for the 95% confidence interval of the population variance ? [4 pts.] Suppose you want to construct a 95% confidence interval for the population standard deviation . What is the lower limit (LL) for the 95% confidence interval of the population standard deviation ? Questions 35 to 37 numerical answers only : you can calculate anywhere (or directly) and place in the designated cells: V3 to V6 respectively M&M Ca popular ca variety of c overall pro orange, 0.1 milk choco [3 pts.] Sup for the col associated select from A Chi-squa A Chi-squa A Chi-squa A Chi-squa A Chi-squa Q38 is MC
Table 4: Q35 - Q37 20 -20.5 12.2 12.6 10.5 -5.8 -18.7 15.3 CV 37 from Chapter 11: concepts covered in Lecture 5, slides 4-15 (Additionally, calculations for a very similar example 11.24 were done in class) from Chapter 12: concepts covered in Lecture 6, slides 3-13 (Additionally, calculations for a very similar example 12.21 were done in class) andy Colors . Mars, Inc. manufactures M&M’s, one of the most andy treats in the world. The milk chocolate candies come in a colors including blue, brown, green, orange, red, and yellow. The oportions for the colors are 0.24 blue, 0.13 brown, 0.20 green, 0.16 13 red, and 0.14 yellow. In a sampling study, several bags of M&M olates were opened and the following color counts were obtained. ppose you want to test the hypothesis that the overall proportions lors are as stated above. Select the correct test scenario with the critical value with the probability of type 1 error as 5%. [ MC: m the drop-down menu] ared test with DF = 6 and a critical value of 14.4494 ared test with DF = 6 and a critical value of 12.5916 ared test with DF = 5 and a critical value of 12.8325 ared test with DF = 5 and a critical value of 11.075 ared test with DF = 5 and a critical value of 1.1455 C : select from the drop-down menu in cell V7
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Questions Answers 35_Var 253.3714286 35_SD 15.9176452 From table 36 1049.548699 1049.467 Chi_(1-0.025) with 7 df 1.69 37 10.52433551 10.52524 Chi_0.025 with 7 df 16.01 38 d. RR is on the upper tail with 5% alpha 11.0704977
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Mgtsc312 F2023 Midterm 1 Saturday, October 21, 2023 Student_ID 1234567 Rand 6.24770417512616 Value from B4 in Rand worksheet - paste as values Questions 1 c. 2 a. 3 72 4 8.875 5 9.14285714285714 6 0.3125 7 0.35 8 0.5625 9 0.08 10 c. 11 0.038759531084514 12 0.824442123911317 13 0.265985529048701 14 0.565685424949238 15 0.922900128256459 16 0.272531793034013 17 5.6 18 0.057982503074452 19 0.91761159639676 20 19.5 21 1.04 22 1.2815515655446 23 1.33281362816638 24 20.8328136281664 25 c. 26 b. 27 0.047696960070847 28 -2.09656967344384 29 0.036031686218234 30 c. 31 -1.6 32 0.877225062070053 33 -1.82393329737338 34 0.089576741341463
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35_Var 253.371428571429 35_SD 15.9176451955504 36 1049.54869896443 37 10.5243355135673 38 d.
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