# Project #43197 - Quantitative methods

The Stalk Market, an independent grocery chain, has been serving and supporting local communities for over 90 years. Its stores offer friendly service and a wide assortment of natural and organic foods. The company is committed to high employee satisfaction and great customer service. In an effort to better understand the characteristics of their workforce, the management has randomly selected 180 employees, who were then

classified according to their job category and gender. The resulting data are summarised in the contingency table below:

 Female Male Total Supervisor 20 15 35 Checkout Operator 35 10 45 Shelf Stacker 10 40 50 Cleaner 32 18 50 Total 97 83 180

(a)

Use Excel to obtain a 100% stacked column chart for the data from the table. What does your chart suggest is the relationship between the type of job and gender?

EXCEL Instructions: Refer to Topic 6 in the Excel Booklet for instructions on how to obtain 100% stacked column chart.

(b) Use the contingency table to calculate the following probabilities; include an appropriate probability statement for each case:

(i).The probability that an employee is female.

(ii).The probability that an employee is male and a checkout operator.

(iii).The probability that an employee is female or a supervisor (or both).

(iv).Given that an employee is male, the probability that he is a shelf stacker.

(v).Given that an employee is a supervisor, the probability that they are female.

(c)Are ‘job category’and ‘gender’independent or dependent? How do you know? Show all calculations that support your answer.

1.

Problems with a telephone line that prevent a customer from receiving or making calls are disconcerting to both the customer and the telephone company. These problems can be of two types: those that are located inside a central office and those located on lines between the central office and the customer’s equipment. The following data represent samples of 20 problems reported to two different offices of a telephone company and the time to clear those problems (in minutes).

 Central Office I Time to clear problems (minutes) 2.52 0.78 0.93 1.02 1.48 1.60 1.75 2.97 3.93 5.45 0.53 0.80 0.97 1.05 1.48 1.60 2.85 3.10 4.15 6.32

 Central Office II Time to clear problems (minutes) 0.08 0.52 0.60 0.65 1.10 1.53 1.92 3.30 3.75 2.23 0.10 0.58 0.60 0.72 1.48 1.65 2.10 3.75 4.02 7,55

(a)

Use EXCEL to obtain a histogram for each central office location.

EXCEL Instructions: Go to the course web site and download the data file for this question, called Phone.xls.

Refer to Topic 6 in the Excel Booklet for instructions on how to obtain and format a histogram; use the bins given in Phone.xls.

(b) Use EXCEL to obtain Descriptive Statistics, Quartile 1and Quartile 3 for each central office location.

EXCEL Instructions: Refer to Topic 7 in the Excel Booklet for instructions on how to obtain Descriptive Statistics and the two quartiles.

(c) Based on the histograms in (a), briefly describe the shape (symmetry, modality and outliers) of the data for each central office location.

Instructions for identifying outliers:

Whether an observation is an outlier is a matter of judgement. One rule commonly used for identifying outliers is the so - called 1.5 × IQR rule. An observation is suspected to be an outlier if it lies more than 1.5 × IQR below the first quartile Q1 or above the third quartile Q3.

Apply this rule to the data from each central office location. Identify suspected outliers (if any) by their exact value(s).

(d) Nominate appropriate measures of centrality and dispersion for the distribution of times to clear problems at each central office location. Give reason(s) for your choice.

For each distribution, give and interpret the values of the summary measures you have chosen.

(e) On the basis of your results of (a)-(d), are there any differences between the two central offices? Write a report based on your findings (at most one page, double - spaced, at least 2cm margins, 12pt Times New Roman or equivalent).

 Subject Mathematics Due By (Pacific Time) 10/13/2014 03:00 am
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