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Industrial customers survey - Global Industrial Sales

Question 1

Sue Taylor, Director of Global Industrial Sales, is concerned by a deteriorating sales trend. While the number of industrial customers is stable at 1,500, they are purchasing less each year. She orders her staff to search for causes of the downward trend by surveying all 1,500 industrial customers. For this study, the set of 1,500 industrial customers is

A)    a parameter.

B)    a sample.

C)    the population.

D)    a statistic.

Question 2

A person has decided to code a particular set of sales data.  A value of 0 is assigned if the sales occurred on a weekday, and a value of 1 if it happened on a weekend. This is an example of

A)    Interval level data. 

B)    Ordinal level data. 

C)    Nominal level data.

D)    Ratio level data.

Question 3

Consider the following frequency distribution:

                                    Class Interval Frequency
                                    10-under 20         15
                                    20-under 30         25
                                    30-under 40         10

What is the relative frequency of the 10-under 20 class interval? A) 0.15. 

B)    0.30. 

C)    0.10. D) 0.20.

Question 4

                   Which situation identifies when to use pie charts and/or bar charts? A) You want to describe a single set of data.

B)    Your data is nominal.

C)    You want to show the number or the percentage of individuals in each category.

D)    All of these choices are true.

Question 5

The sum of the relative frequencies for all classes in a histogram is always equal. Suppose a market survey of 200 consumers was conducted to determine the likelihood of each consumer purchasing a new computer next year. The data were collected based on the age of the consumer and are shown below:

Age BracketIntent to Purchase
 Computer within 1 year
<2554
25-3457
35-4449
45-5429
>5511
Total Surveyed200

Using the table above, which of the following statements is true?

A)    Younger consumers are more likely to purchase a computer next year.

B)    Older consumers are more likely to purchase a computer next year.

C)    There does not appear to be a relationship between age and purchasing a computer.

D)    Individuals between 25 and 34 are most likely to purchase a new computer next year.

Question 6

The relationship between two interval variables is graphically displayed by a

A)    scatter diagram

B)    histogram

C)    bar chart

D)    pie chart

Question 7

A statistics student made the following scores on 7 tests: 76, 82, 92, 95, 79, 86, and 92.   What is the median?

A) 79 B) 82

C)    86

D)    92

Question 8

The average score for a class of 30 students was 75. The 15 male students in the class averaged 70. Therefore the 15 female students in the class averaged:

A)    85

B)    80 C) 75

D) 70

Question 9

A commuter travels many miles to work each morning.  She has timed this trip 5 times during the last month.  The time (in minutes) required to make this trip was 38, 33, 36, 47, and 41.  What is the variance for this sample data?

A)    28.5

B)    11

C)    22.8

D)    5.34

Question 10

Let F be the event that a student is enrolled in a finance course, and let S be the event that a student is enrolled in a statistics course.  It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in a statistics course.  Included in these numbers are 15% of students who are enrolled in both statistics and finance.  If a student is randomly selected, what is the probability that the student is enrolled in either finance or statistics or both?

A)    0.15

B)    0.75 C) 0.60 D) 0.55

Part B: Completion Questions [2 marks for each question, total 20 marks]

Question 1

There are two branches of the statistics; the _________________ and the ____________________.

Question 2

According to the Empirical Rule, if the data form a bell shaped normal distribution, approximately ____________________ percent of the observations will be contained within 2 standard deviations around the mean. If the data do not form a bell shaped normal distribution, approximately ____________________ percent of the observations will be contained within 2 standard deviations around the mean.

Question 3

The method used to find the best fitting line through the observations is called the ____________________ method.

Question 4

If two events are mutually exclusive, the probability of their intersection is  equal to ___________________.

Question 5

The total area under f(x) for a continuous random variable must equal ________.

Question 6

Suppose X is a normal random variable with mean 70 and standard deviation 3. Then P(X = 72) = ____________________.

Question 7

Because the value of the ____________________ varies from sample to sample, we can regard it as a new random variable, created by sampling.

Question 8

The F value in one-way ANOVA is the ratio of ____________________ and____________________.

Question 9

When the population standard deviation is unknown and the population is normal, the test statistic for testing hypotheses about ? is the ____________________-distribution with ____________________ degrees of freedom.

Question 10

SSE stands for ____________________ of squares for ____________________.

Part C: Calculation Questions [70 Marks]

Question 1 [8 marks]

Part a) 

Given a normal distribution with ?=100 and ?=10. There is a 65% chance that a randomly selected item is above what value? (4 marks)

Part b) 

An operations manager selected a sample of 64 of waiting times for walk-in customers. If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes,

What is the probability that sample mean is less than 16 minutes? (4 marks)

Question 2 [6 marks]

The Australian Journal of Statistics reported that 40% of all workers say they would change jobs for slightly higher pay. In addition, 90% of companies say that there is a shortage of qualified job candidates. Suppose 18 workers are randomly selected and asked if they would change jobs for slightly higher pay. 

i)                   What is the probability that nine or more say yes? (3 marks)

ii) What is the probability that five, six, or seven say yes? (3 marks)

Question 3 [12 marks] Part a)                                                                                                           (4 marks)

The mean of a sample of 25 observations was calculated as 500. The sample was randomly drawn from a normal population whose standard deviation is 15. Estimate the population mean with 95% confidence.

Part b)                                                                                                              (8 marks)

The following sample of 16 measurements was selected from a population that is approximately normally distributed.

                                          61        85        92        77        83        81        75        78

                                          95        87        69        74        76        84        80        83

Construct a 90% confidence interval for the population mean. 

 

 

 

 

 

 

 

Question 4 [16 marks] 

A random sample of 16 women and 7 men employed were selected in a company. The women took an average of 25 hours of personal time per year with a standard deviation of 3 hours. The men took an average of 22 hours of personal time per year with a standard deviation of 4 hours. Manager believes that women take more personal time than men. Assuming equal population standard deviations, test at the 1% significance level whether the women (population 1) have taken significantly more personal time than men (population 2). (Write all 8 steps of hypothesis testing).

Question 5 [8 marks]

The following lists the 10 largest automakers in the world and the number of vehicles produced by each in a recent year.  

                 Auto Manufacturer                Production (millions)

Toyota Motor Corp.9.37
General Motors 8.9
Volkswagen AG 6.19
Ford Motor Co. 5.96
Hyundai-Kia Automotive Group 4.96
Honda Motor Co. Ltd. 3.83
Nissan Motor Co. 3.68
PSA/Peugeot-Citreon SA 3.43
Chrysler LLC 2.68
Fiat S.p.A. 2.62

i) Find the mean and median (2 marks) ii) Find the third quartile Q3 (2 marks) iii) Find the 20th percentile P20 (2 marks) iv) Find the 60th percentile P60 (2 marks) Question 6 [9 marks]

A corporation owns several shops. The strategic planner for the corporation believes dollars spent on advertising might be a predictor of total sales dollars. As an aid in longterm planning, she gathers the following sales and advertising information from several of the shops for 2016 ($ millions).            

Advertising                             Sales  

12.5     148  3.7           55 

21.6     338       60.0    994       

37.6                                             541                      

6.1                                                 89                      

16.8                                             126                      

41.2                                             379

Develop the equation of the simple regression line to predict sales from advertising expenditures using these data. 

Question 7 [11 marks]

A market analyst is looking at product prices for three fruit juice bar companies located in different cities. She collects sample information from each company in order to conduct an ANOVA test (Excel output provided below). Examine whether the price of fruit juice bar in all three cities is different.  Use 5% level of significance (Write all 6 steps of hypothesis testing). 

             Anova: Single Factor                                                                                                             

            SUMMARY                                                                                                                            

   GroupsCountSumAverageVariance
Boost juice535.67.123.852
Naked juice532.5    6.50          0.760
Funky juice538.57.701.285

ANOVA

Source of VariationSSDfMSF                                        
Between Groups3.60133321.800.916                        
Within Groups23.588      121.9657            
Total27.1893314             

Formulas

M.A.D.  =  ?|#$#?|    ?(       ?         |           ?) =   &

            x-                  !"#                     x- p - p

z = s ?= $       t = s     z =             n  n

s s

xz              xt     t = (X1 - X2) (- - 1         2)      z n        n      S12               S2

+ 2 n1 n2

                                  (x1 -x2)-(1 -2)                               SS

    t =       2             2                           b1  =    xy s1 (n1 -1)+s2 (n2 -1) 1 + 1  SSx n1 +n2 -2  n1           n2

             ?% " ?$ ?"-                     ?- = ?% + ?$?

             ? = #?$            

                             !    )$%#

= (X1 - X2) (- 1 - 2) s s12 + 22 n1     n2

=xy-xn2y

x2 - (nx)

t distribution Critical values  

Industrial customers survey - Global Industrial Sales

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