Need help in Statistics

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Please answer all the questions correctly in the paper. will need it for exam revision.

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BUS105e Examination – January Semester 2018 Statistics Thursday, 17 May 2018 10:00 am – 12:00 pm ____________________________________________________________________________________ Time allowed: 2 hours ____________________________________________________________________________________ INSTRUCTIONS TO STUDENTS: 1. This examination contains FOUR (4) questions and comprises SEVENTEEN (17) printed pages (including cover page, Appendices A and B). 2. You must answer ALL questions. 3. All answers must be written in the answer book. 4. This is a closed-book examination. At the end of the examination Please ensure that you have written your examination number on each answer book used. Failure to do so will mean that your work cannot be identified. If you have used more than one answer book, please tie them together with the string provided. THE UNIVERSITY RESERVES THE RIGHT NOT TO MARK YOUR SCRIPT IF YOU FAIL TO FOLLOW THESE INSTRUCTIONS. BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 1 of 17 You must answer ALL the questions. (Total 100 marks) Question 1 A property agent has collected selling price information on the homes sold in the last month. Below are two graphs he has used to describe the data: (a) Describe the type of statistical charts used above, and explain why the two charts look differently. Interpret the selling price information shown in the two charts. (6 marks) (b) Identify the number of homes that were sold for less than S$200,000. (4 marks) (c) Estimate the percentage of homes that were sold for more than S$220,000. (5 marks) BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 2 of 17 The summary statistics of the selling prices produced by Excel are shown below: (d) Explain why the mean is bigger than the median. (4 marks) (e) Interpret the skewness. What does it suggest? (6 marks) Question 2 Catherine Ng is a car seller. Over the years, she has developed the following probability distribution for the number of cars she expects to sell on Saturday. Number of cars sold, X Probability, P(X) 0 0.10 1 0.20 2 0.35 3 ? 4 0.10 More than 4 0.00 Table 2-1 (a) Identify the probability that Catherine can expect to sell three cars on Saturday. (4 marks) (b) On average, how many cars can Catherine expect to sell on Saturday? (4 marks) (c) Identify the probability that Catherine can expect to sell at least two cars on Saturday. (4 marks) BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 3 of 17 (d) Calculate the variance and standard deviation of the distribution. (8 marks) (e) Assume that there is another car seller Tony Lee who can sell on average 2.05 cars on Saturday and the standard deviation for his sales distribution is 1.91 cars. Interpret and compare the sales performance of Catherine and Tony. (5 marks) Question 3 (a) The birth weights (in grams) of 30 baby boys who were recently born in the Rose Women’s and Children’s Hospital are: 3982 3686 4011 3680 3175 3939 3684 3657 4080 3789 3368 3698 3105 3257 3168 3089 3257 3542 3159 3610 3068 3501 3421 3330 3452 3433 3681 3524 3714 3257 The summary statistics of the birth weights of 30 baby boys produced by Excel are reported below: Table 3-1 BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 4 of 17 Assume that birth weight of baby boy born in the Rose Women’s and Children’s Hospital (denote by y) follows a normal distribution with a mean of 3400 grams and a standard deviation that agrees with the standard deviation in Table 3-1. (i) State the 95% confidence interval for the mean weight of baby boys born recently, based on Table 3-1. (4 marks) (ii) Write down the value of y where y is 1 standard deviation smaller than the population mean. Identify and estimate the probability that the birth weight of a randomly chosen baby boy born in the Rose Women’s and Children’s Hospital is greater than this value of y. (8 marks) (iii) Use the Central Limit Theorem to estimate the probability that the sample mean is greater than or equal to the mean as shown in Table 3-1. (5 marks) (b) The weights (in grams) of 30 baby girls who were recently born in the Rose Women’s and Children’s Hospital are: 3104 3269 2991 3067 3681 3329 3106 3527 4023 3675 3362 3510 3288 3675 3266 3612 3250 3528 3121 4001 3065 3259 3470 3159 3568 3254 3304 3505 3662 3253 The summary statistics of the birth weights of 30 baby girls produced by Excel are reported below: Table 3-2 BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 5 of 17 To examine whether the mean weights of baby boys and baby girls born recently in the Rose Women’s and Children’s Hospital are the same at the 5% significance level, the following Excel report is produced. t-Test: Two-Sample Assuming Unequal Variances W_boy W_girl Mean 3511 3396 Variance 84160 70017 Observations 30 30 Hypothesized Mean Difference 0 df 58 t Stat 1.596 P(T<=t) one-tail 0.058 t Critical one-tail 1.672 P(T<=t) two-tail 0.116 t Critical two-tail 2.002 Table 3-3 Apply an appropriate hypothesis testing method to compare the two sample means and answer the question whether the two means are the same. Select and state the null and alternative hypotheses and state the conclusion of the hypothesis testing. (8 marks) BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 6 of 17 Question 4 Jenson Tan is the HR manager at company Nilect. As part of his yearly report to the CEO, he is required to present an analysis of the salaried employees. There are over 10,000 employees in Nilect and Jenson does not have sufficient resources to gather information on each salaried employee. As such, he selected a random sample of 30 employees for analysis. For each employee, he recorded monthly salary, service at Nilect in months, years of education obtained, and whether the employee has a technical or clerical job (1=technical job, 0=clerical job). Data collected are shown below: Sampled Employee 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Monthly Salary (S$) 3538 3480 3882 3582 4002 3748 3591 3625 3368 4025 4468 4926 5102 4514 4398 3106 4200 3500 3624 3972 2900 3500 4256 4124 4058 3762 3394 5130 5674 4620 Length of Service (months) 38 74 54 90 60 51 16 21 31 43 53 29 65 68 36 35 26 25 19 46 12 16 40 49 46 49 9 64 72 40 Years of Education 15 12 16 14 16 15 16 18 15 16 16 18 16 16 20 13 20 16 16 15 14 16 16 16 16 14 16 18 18 18 Table 4-1 BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 7 of 17 Job Type 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 1 Excel is applied to perform the multiple linear regression analysis on the data. The following report is produced: SUMMARY OUTPUT Regression Statistics Multiple R 0.86413319 R Square 0.74672617 Adjusted R Square 0.717502266 Standard Error 339.3322148 Observations 30 ANOVA df 3 26 29 Regression Residual Total SS 8826623.148 2993805.152 11820428.3 MS 2942207.716 115146.352 F 25.55189691 Significance F 6.45757E-08 Intercept Coefficients -1207.716874 Standard Error 639.285171 t Stat -1.889167665 P-value 0.070071535 Lower 95% -2521.786362 Upper 95% 106.352615 Lower 95.0% -2521.786362 Upper 95.0% 106.352615 Length of Service (months) 20.11282585 3.216644361 6.252735332 1.28698E-06 13.50091867 26.72473303 13.50091867 26.72473303 Years of Education 277.5953655 37.85933163 7.332283839 8.7095E-08 199.7743948 355.4163362 199.7743948 355.4163362 Job Type -207.6387994 131.6338266 -1.577396972 0.126795058 -478.216005 62.93840621 -478.216005 62.93840621 Table 4-2 Please answer the following questions with reference to Table 4-2: (a) Describe the relationship between monthly salary (Y), service length (X 1 ), years of education (X 2 ) and job type (X 3 ) by writing down the linear equation. Interpret how the three (3) independent variables affect the dependent variable Y. (5 marks) (b) State the coefficient of multiple determination and the adjusted coefficient of multiple determination. How may we interpret these coefficients and why are they different? (5 marks) (c) Discuss and estimate the monthly salary of an employee who has a master degree (18 years of education) and has been working as a technical staff in the company for 26 months. (5 marks) BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 8 of 17 (d) Execute a hypothesis test to determine whether all regression coefficients are zero at the 5% significance level. Write down your steps carefully. (5 marks) (e) Execute a hypothesis test to determine whether it makes a difference to have a technical or a clerical job at the 5% significance level. Write down your steps carefully. (5 marks) ----- END OF PAPER ----- BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 9 of 17 Appendix A: Formula sheet Population Mean µ= ∑X N [1-1] Sample Mean X = ∑X n [1-2] Mean of a discrete random variable Range [1-3] Range = Largest value – Smallest value [1-4] Population variance σ2 = ∑( X − µ ) 2 N [1-5] Population standard deviation σ= ∑( X − µ ) 2 N [1-6] Sample variance s2 = ∑( X − X ) 2 n −1 [1-7] s= ∑( X − X ) 2 n −1 [1-8] Sample standard deviation Variance of a discrete random variable Standard deviation of a discrete random variable BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 [1-9] [1-10] Page 10 of 17 X −µ Standard normal value z= Standard error of mean σx = z-value, µ and σ known z= [2-1] σ σ [3-1] n X −µ [3-2] σ n Confidence interval for µ , with σ known X ±z Confidence interval for µ , with σ unknown X ±t Testing a mean, σ known z= σ [4-1] n s [4-2] n X −µ [5-1] σ n Testing a mean, σ unknown t= X −µ s [5-2] n Sample proportion p= X n BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 [6-1] Page 11 of 17 Appendix B Source: Basic Statistics for Business & Economics by Lind Douglas A., Marchal William G. & Wathen, Samuel A. (2012) 8th Edition, McGraw-Hill BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 12 of 17 BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 13 of 17 Source: Basic Statistics for Business & Economics by Lind Douglas A., Marchal William G. & Wathen, Samuel A. (2012) 8th Edition, McGraw-Hill BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 14 of 17 Source: Basic Statistics for Business & Economics by Lind Douglas A., Marchal William G. & Wathen, Samuel A. (2012) 8th Edition, McGraw-Hill BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 15 of 17 Source: Basic Statistics for Business & Economics by Lind Douglas A., Marchal William G. & Wathen, Samuel A. (2012) 8th Edition, McGraw-Hill BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 16 of 17 Source: Basic Statistics for Business & Economics by Lind Douglas A., Marchal William G. & Wathen, Samuel A. (2012) 8th Edition, McGraw-Hill BUS105e Copyright © 2018 Singapore University of Social Sciences (SUSS) Examination – January Semester 2018 Page 17 of 17 ...
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Tutor Answer

DonKobong
School: Cornell University

Attached.

Running head: STATISTICS

Statistics
Name
Institution

STATISTICS
QUESTION ONE
a)

The type of statistical chart used above is histograms. They represent continuous

data where the numbers represented can take any values of number houses in the given range.
However, the first graph, the data has been represented by the frequency of particular phenomena
by using width $50000. It shows selling price that has a range of more than $50000 between
subsequently fixed intervals. The second graph has data represented using categories with a
width of $25000. It shows an interval of $25000 being used in the continuous data to indicate the
range in selling price. In both the first and the second graph, the bars are adjacent to one another.
The histograms are never drawn with spaces between the bars. The data in both graphs
are continuous. Since the first graph has a higher width range, they accumulate a higher number
of homes that are sold and hence they appear bigger compared to the second graph. The second
histogram had precise readings and inferences and give deeper ideas due to its smaller intervals.
Alternatively, the second graph can be said to have used the midpoints of the first graph. The
first graph has used five classes while the second has used eight classes. The maximum selling
price of between 150000-200000 dollars was the highest number with 38 being sold in the first
histogram while the second histogram had 26 houses at the selling prices that range between
175000-200000 dollar ranges.
b)

The number of homes sold for less than S$200000 from both histograms is 42. 38+4

=42 from the first histogram and 4+12+26= 42 from the second histogram.
c)

The number of houses that were sold for a selling price that is less than $200000 will

be added together using figures obtained from the histogram. The added results will then be
divided by the overall house's total that was sold and then the result will be multiplied by 100 to
obtain the percentage as shown below.

STATISTICS
[(13...

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Anonymous
Good stuff. Would use again.

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