Managerial Statistics Assignment- Regent Business School

QUESTION ONE      [25]
The following information was gathered from 100 families in rural KZN with regard to their weekly incomes.
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1.1 Draw the downward sloping (<) ogive using the frequency distribution.     (3)
1.2 Calculate the mean weekly income.     (4)
1.3 Calculate the median income.     (3)
1.4 Calculate the mode.     (3)
1.5 Calculate the standard deviation.     (6)
1.6 Calculate the interquartile range     (6)
QUESTION TWO     [25]
2.1 On weekdays from 11: 30 am to 2:00 pm customers arrive at a hotdog street vendor at the rate of 25 per 30 minute interval. Assume that this process can be well modeled by the Poisson distribution.
2.1.1 What is the average time between customer arrivals?     (2)
2.1.2 What is the probability that the vendor will have to wait no more than 3 minutes for a customer?     (3)
2.2 In a survey conducted by the Society for human Resource Management, 68% of workers said that employers have the right to monitor their telephone use. Suppose that a random sample of 20 workers is selected, and they are asked if employers have the right to monitors telephone use. What is the probability that:
 2.2.1 5 or less of the workers agree?     (3)
2.2.2 15 or less of the workers agree?     (4)
2.3 The birth weights of female babies born at a certain hospital are approximately normally distributed with a mean of 3.40kg and a standard deviation of 0.48 kg. Find the proportion of female babies who have birth weights in the following ranges:
2.3.1 less than 3.94 kg     (2)
2.3.2 more than 2.96 kg     (3)
2.33 between 2.5 kg and 3.70 kg      (3)
2.4 Referring to question 2.3 above, if the Babies are to be defined as ‘underweight’ when they are in the lowest 5%of the distribution, what will be the cut-off point defining underweight?     (5)
QUESTION THREE     [20]
3.1 A shopkeeper observes the number of cans of cool drink of various types sold during one week. The results are displayed in the table below:

 

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Test with 5% level of significance if there is any relationship between the days of the week and popularity of the various types of soft drink    (12)

3.5 The results of an annual claimant satisfactory Survey of policyholders who have had claim with State Farm Insurance Company revealed a 90%
satisfactory rate for claim rate for service. To check the accuracy of this claim, a random sample of State farm claimants was asked to rate whether they were satisfied with the quality of the service. The number who were satisfied was 153, unsatisfied 24. Test at the 5% significance level that the satisfaction rate is less than 90%.     (8)
QUESTION FOUR     [30]
4.1 The data below are the quarterly demand levels for electricity (in 1000 megawatts) in Cape Town from 1988 to 1991.

 

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You are required to:
4.1.1 Obtain a 4-terms moving average trend.     (4)
4.1.2 Find the seasonal variations using the multiplicative model.     (8)
4.2 In an attempt to analyze the relationship between advertising and sales, the owner of a furniture store recorded the monthly advertising budget (in thousand rand) and the sales ( in millions rand) for a sample of 12 months. The data is listed below.

 

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Identify the Dependent and the independent variables.     (1)
4.2.2 Draw a scatter diagram. Does it appear that adverting and sales are linearly related?     (3)
4.2.3 Calculate Pearson’s correlation coefficient and interpret it.     (5)
4.2.4 Calculate the (least square) regression line and interpret the coefficient (Intercept and the slope).     (7)
4.1.5 Estimate the sales if the company spends R150000 on advertising.      (2)

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