Business Statistics I CQMS102 – Test 1REVIEW PROBLEMSQuestion1.In a survey the respondent is asked to report the amount of income tax paid in 2010. The scale of measurement used is:a) Nominalb) Intervalc) Ratiod) Ordinale) None of the aboveQuestion2. Consider the following questions being asked on a survey. What is the measurement scale of the response data?(a) Ordinal(b) Nominal(c) Interval(d) Ratio â Discrete(e) Ratio – Continuous1) What was the rating of the hotel that you last stayed in? Ordinala) Dissatisfiedb) Somewhat Dissatisfiedc) Somewhat satisfiedd) Satisfiede) Very good2) What is your marital status? Nominal1=Married; 2=Common Law; 3=Widowed; 4=Divorced; 5=Single3) What is the major that you are studying? Nominala) Mathb) Physicsc) Chemistryd) Biologye) History4) What is the postal code? Nominal5) Which letter grade did you get on your Chemistry course last term? Ordinal6) What is the color of your eyes? Nominal7) What is the color of your car? Nominal8) Where is your hometown? Nominal9) How many courses are taking this term? Ratio â Discrete10) How much time do you spend on shopping each week? Ratio – Continuous11) What was the lowest temperature in .gif”>in the city you are living last month? Interval12) How many children do you intend to have? Ratio â Discrete13) How many languages can you speak? Ratio â Discrete14) Which language is your native language? Nominal15) Where were you born? Nominal16) What is your weight? Ratio – Continuous17) How long does it take for you to walk from your home to Ryerson? Ratio – ContinuousNOTE: Questions 3 â 4 are based on the following information.The following data represents the heights (m) for a sample of 11 boys at age 12.1.38, 1.43, 1.25, 1.47, 1.29, 1.54, 1.37, 1.25, 1.53, 1.45, 1.29Question3. If you were to construct a stem-and-leaf display using the rules discussed in lectures for the above data, how many stems should your final stem-and-leaf display have?a) 7 b) 8 c) 6 d) 9 e) None of theseQuestion4. Based on the stem-and-leaf display (using the rules discussed in lectures) for the above data, how many leaves would there be on the second stem of your stem-and-leaf display?a) 4 b) 0 c) 2 d) 3 e) None of theseNOTE: Questions 5 – 8 are based on the following information.The following data represents the heights (m) for a sample of 12 boys at age 12.1.38, 1.43, 1.25, 1.47, 1.29, 1.54, 1.37, 1.25, 1.53, 1.45, 1.29, 1.41Question5. If you were to construct a frequency distribution using the rules discussed in lectures for the above data, what would the class width (in thousand dollars) be?a) 1.0 b) 0.05 c) 0.50 d) 0.10 e) 0.025Question6. If you were to construct a frequency distribution using the rules discussed in lectures for the above data, how many classes are there in the frequency distribution?a) 4 b) 5 c) 8 d) 6 e) 10Question7. Based on the frequency distribution using the rules discussed in lectures for the above data, what is the relative frequency of the fourth class? (The answers provided below are rounded to three decimal places).a) 0.250 b) 0.333 c) 0.375 d) 0.167 e) None of theseQuestion8. Based on the frequency distribution using the rules discussed in lectures for the above data, what is the cumulative percentage of up to and including the third class? (The answers provided below are rounded to two decimal places).a) 16.67% b) 33.33% c) 50.00% d) 46.67% e) None of theseUse the following data for questions 9 to 11 inclusive.The following table represents the distribution of the income ($1000) in 2011 for a sample of households in Toronto.Table 1Income ($1000)Number of households20 and under 303730 and under 402240 and under 504550 and under 60560 and under 702070 and under 801180 and under 9015Question9. The cumulative relative frequency of the households in this sample, whose incomes in 2011 are lower than $70,000, isa) 12.9% b) 16.8% c) 73.5% d) 83.2% e) 80.3%Question 10. The relative frequency of the households in this sample, whose incomes in 2011 are higher than $50,000, is (rounded to three decimal places):a) 0.671b) 0.032c) 0.329d) Cannot be determined from the tablee) None of the aboveQuestion11.The class width (in $1000) for the classes in this table is:a) 10,000 b) 5,000 c) 10 d) 5 e) 25Note: Questions 12-14 are based on the following informationForty-five students wrote the PCS105 midterm test last week. The following stem-and-leaf display shows the grades of students who failed PCS105 midterm test last week.Stem(.gif”>)Leaf017 80 1 2122335 90 05 5 68 941 3Question12.What is the maximum value in the above data?a) 40.3 b) 4.3 c) 4.03 d) 43 e) 41.3Question13.How many students passed the last weekâs PCS105 midterm test?a) 15 b) 16 c) 23 d) 29 e) 25Question14.What is the failure rate of this test?a) 64.44% b) 35.56% c) 25.72% d) 24.73% e) 14.32%Note: Questions 15 â 18 are based on the following Ogive.The length of stay, t days, that each of 500 guests stayed at a five star hotel was recorded and the results used to construct the Ogive below. Note that the first class is â0 and under 5â and the last class is â35 and under 40â..gif”>Question15.How many guests have stayed in this hotel at least 20 days?a) 300 b) 200 c) 150 d) 350 e) 100Question16.How many guests (in percentage) stayed in this hotel 15 days or more?a) 40% b) 60% c) 70% d) 35% e) cannot be determinedQuestion17.Find the approximate average length of stay per guest.a) 18 b) 19 c) 19.5 d) 18.5 e) cannot be answeredQuestion18.Find the 70th percentile:a) 35 b) 25 c) 15 d) 22.5 e) cannot be answeredQuestion19. Listed below are the annual union fees paid by a simple random sample of Ryersonians.$400, $383.5, $350.7, $232.5, $360, $1102.43, $421, $810.09, $122.33.What is the variance of the above data? (Rounded to two decimal places)81530.8166754.4491721.76285.54302.86Questions 20-21 are based the following information. The answers are rounded to one decimal place.Forty-five students wrote the PCS105 midterm test last week. The following stem-and-leaf display shows the grades of students who failed PCS105 midterm test last week.Stem(.gif”>)Leaf017 80 1 2122335 90 05 5 68 941 3Question20. The 75th percentile of the above data is:26 b. 38 c. 32 d. 25.5 e. 36.5Question21. The range of the above data is:20.5 b. 35 c. 26 d. 25 e. 15Use the following data for Question 22.Question22. The following table shows some data regarding the top 5 grocery chains in Toronto.Table 1ChainsNumber of StoresAnnual Revenue per store($000)Total Profit ($Million)A336980022B214298015C253890019D122890512E255430026a) What is the overall mean annual revenue per store for the five chains shown? (50714.14 thousand dollars)b) What is the standard deviation of the annual revenue per store? (14079.14 thousand dollars)c) What is the overall mean profit per store? (0.81 Million dollars)d) What is the overall mean profit per chain for the five chains shown? (18.8 Million dollars)e) What is the standard deviation of the profit per chain? (5.54 Million dollars)Question23..gif”>.gif”>Answer is BQuestion24. Construct a bar chart that represents the data in Question 23..gif”>Question25. Twenty-nine executives reported the number of telephone calls made during a randomly selected week as shown here.24 15 12 8 56 12 18 12 15 43 10 155 22 36 29 35 24 8 33 58 32 46 197 16 26 29 53Find the mean, median and mode. Find the 42th percentile.Mean=24.76Median=22Mode=12, 15.gif”>Questions 26 – 28 are based on the following information.Warren County Telephone Company claims in its annual report that “the typical customer spends $75 per month on local and long-distance service.” A sample of 25 subscribers revealed the following amounts (in dollars) spent last month.72, 77, 70, 80, 90, 78, 65, 93, 69, 94, 73, 96, 80,66, 85, 67, 72, 85, 74, 77, 64, 91, 79, 68, 86Question26.What is the median of the observations?a) 78 b) 77.5 c) 77d) 74 e) 75Question27.What is the 40th percentile of the observations?a) 73 b) 73.5 c) 94 d) 74 e) 68Question28.What is/are the mode(s) of the observations?a) 72b) 77c) 80

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Business Statistics I CQMS102 – Test 1REVIEW PROBLEMSQuestion1.In a survey the respondent is asked to report the amount of income tax paid in 2010. The scale of measurement used is:a) Nominalb) Intervalc) Ratiod) Ordinale) None of the aboveQuestion2. Consider the following questions being asked on a survey. What is the measurement scale of the response data?(a) Ordinal(b) Nominal(c) Interval(d) Ratio â Discrete(e) Ratio – Continuous1) What was the rating of the hotel that you last stayed in? Ordinala) Dissatisfiedb) Somewhat Dissatisfiedc) Somewhat satisfiedd) Satisfiede) Very good2) What is your marital status? Nominal1=Married; 2=Common Law; 3=Widowed; 4=Divorced; 5=Single3) What is the major that you are studying? Nominala) Mathb) Physicsc) Chemistryd) Biologye) History4) What is the postal code? Nominal5) Which letter grade did you get on your Chemistry course last term? Ordinal6) What is the color of your eyes? Nominal7) What is the color of your car? Nominal8) Where is your hometown? Nominal9) How many courses are taking this term? Ratio â Discrete10) How much time do you spend on shopping each week? Ratio – Continuous11) What was the lowest temperature in .gif”>in the city you are living last month? Interval12) How many children do you intend to have? Ratio â Discrete13) How many languages can you speak? Ratio â Discrete14) Which language is your native language? Nominal15) Where were you born? Nominal16) What is your weight? Ratio – Continuous17) How long does it take for you to walk from your home to Ryerson? Ratio – ContinuousNOTE: Questions 3 â 4 are based on the following information.The following data represents the heights (m) for a sample of 11 boys at age 12.1.38, 1.43, 1.25, 1.47, 1.29, 1.54, 1.37, 1.25, 1.53, 1.45, 1.29Question3. If you were to construct a stem-and-leaf display using the rules discussed in lectures for the above data, how many stems should your final stem-and-leaf display have?a) 7 b) 8 c) 6 d) 9 e) None of theseQuestion4. Based on the stem-and-leaf display (using the rules discussed in lectures) for the above data, how many leaves would there be on the second stem of your stem-and-leaf display?a) 4 b) 0 c) 2 d) 3 e) None of theseNOTE: Questions 5 – 8 are based on the following information.The following data represents the heights (m) for a sample of 12 boys at age 12.1.38, 1.43, 1.25, 1.47, 1.29, 1.54, 1.37, 1.25, 1.53, 1.45, 1.29, 1.41Question5. If you were to construct a frequency distribution using the rules discussed in lectures for the above data, what would the class width (in thousand dollars) be?a) 1.0 b) 0.05 c) 0.50 d) 0.10 e) 0.025Question6. If you were to construct a frequency distribution using the rules discussed in lectures for the above data, how many classes are there in the frequency distribution?a) 4 b) 5 c) 8 d) 6 e) 10Question7. Based on the frequency distribution using the rules discussed in lectures for the above data, what is the relative frequency of the fourth class? (The answers provided below are rounded to three decimal places).a) 0.250 b) 0.333 c) 0.375 d) 0.167 e) None of theseQuestion8. Based on the frequency distribution using the rules discussed in lectures for the above data, what is the cumulative percentage of up to and including the third class? (The answers provided below are rounded to two decimal places).a) 16.67% b) 33.33% c) 50.00% d) 46.67% e) None of theseUse the following data for questions 9 to 11 inclusive.The following table represents the distribution of the income ($1000) in 2011 for a sample of households in Toronto.Table 1Income ($1000)Number of households20 and under 303730 and under 402240 and under 504550 and under 60560 and under 702070 and under 801180 and under 9015Question9. The cumulative relative frequency of the households in this sample, whose incomes in 2011 are lower than $70,000, isa) 12.9% b) 16.8% c) 73.5% d) 83.2% e) 80.3%Question 10. The relative frequency of the households in this sample, whose incomes in 2011 are higher than $50,000, is (rounded to three decimal places):a) 0.671b) 0.032c) 0.329d) Cannot be determined from the tablee) None of the aboveQuestion11.The class width (in $1000) for the classes in this table is:a) 10,000 b) 5,000 c) 10 d) 5 e) 25Note: Questions 12-14 are based on the following informationForty-five students wrote the PCS105 midterm test last week. The following stem-and-leaf display shows the grades of students who failed PCS105 midterm test last week.Stem(.gif”>)Leaf017 80 1 2122335 90 05 5 68 941 3Question12.What is the maximum value in the above data?a) 40.3 b) 4.3 c) 4.03 d) 43 e) 41.3Question13.How many students passed the last weekâs PCS105 midterm test?a) 15 b) 16 c) 23 d) 29 e) 25Question14.What is the failure rate of this test?a) 64.44% b) 35.56% c) 25.72% d) 24.73% e) 14.32%Note: Questions 15 â 18 are based on the following Ogive.The length of stay, t days, that each of 500 guests stayed at a five star hotel was recorded and the results used to construct the Ogive below. Note that the first class is â0 and under 5â and the last class is â35 and under 40â..gif”>Question15.How many guests have stayed in this hotel at least 20 days?a) 300 b) 200 c) 150 d) 350 e) 100Question16.How many guests (in percentage) stayed in this hotel 15 days or more?a) 40% b) 60% c) 70% d) 35% e) cannot be determinedQuestion17.Find the approximate average length of stay per guest.a) 18 b) 19 c) 19.5 d) 18.5 e) cannot be answeredQuestion18.Find the 70th percentile:a) 35 b) 25 c) 15 d) 22.5 e) cannot be answeredQuestion19. Listed below are the annual union fees paid by a simple random sample of Ryersonians.$400, $383.5, $350.7, $232.5, $360, $1102.43, $421, $810.09, $122.33.What is the variance of the above data? (Rounded to two decimal places)81530.8166754.4491721.76285.54302.86Questions 20-21 are based the following information. The answers are rounded to one decimal place.Forty-five students wrote the PCS105 midterm test last week. The following stem-and-leaf display shows the grades of students who failed PCS105 midterm test last week.Stem(.gif”>)Leaf017 80 1 2122335 90 05 5 68 941 3Question20. The 75th percentile of the above data is:26 b. 38 c. 32 d. 25.5 e. 36.5Question21. The range of the above data is:20.5 b. 35 c. 26 d. 25 e. 15Use the following data for Question 22.Question22. The following table shows some data regarding the top 5 grocery chains in Toronto.Table 1ChainsNumber of StoresAnnual Revenue per store($000)Total Profit ($Million)A336980022B214298015C253890019D122890512E255430026a) What is the overall mean annual revenue per store for the five chains shown? (50714.14 thousand dollars)b) What is the standard deviation of the annual revenue per store? (14079.14 thousand dollars)c) What is the overall mean profit per store? (0.81 Million dollars)d) What is the overall mean profit per chain for the five chains shown? (18.8 Million dollars)e) What is the standard deviation of the profit per chain? (5.54 Million dollars)Question23..gif”>.gif”>Answer is BQuestion24. Construct a bar chart that represents the data in Question 23..gif”>Question25. Twenty-nine executives reported the number of telephone calls made during a randomly selected week as shown here.24 15 12 8 56 12 18 12 15 43 10 155 22 36 29 35 24 8 33 58 32 46 197 16 26 29 53Find the mean, median and mode. Find the 42th percentile.Mean=24.76Median=22Mode=12, 15.gif”>Questions 26 – 28 are based on the following information.Warren County Telephone Company claims in its annual report that “the typical customer spends $75 per month on local and long-distance service.” A sample of 25 subscribers revealed the following amounts (in dollars) spent last month.72, 77, 70, 80, 90, 78, 65, 93, 69, 94, 73, 96, 80,66, 85, 67, 72, 85, 74, 77, 64, 91, 79, 68, 86Question26.What is the median of the observations?a) 78 b) 77.5 c) 77d) 74 e) 75Question27.What is the 40th percentile of the observations?a) 73 b) 73.5 c) 94 d) 74 e) 68Question28.What is/are the mode(s) of the observations?a) 72b) 77c) 80

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