QUESTION 1
In Switzerland, an Insurance agency retail life insurance called Savings life Insurance (SLI). The skill to deliver approved policies to the customers in a timely manner is critical to profitability of the Insurance agency. Through a period of a month, a random sample of 27 approved policies was selected, and the following total processing times in days were recorded-
73 19 16 64 28 28 31 90 60 56 31 56 22 18 45 48 17
17 17 91 92 63 50 51 69 16 17
a) Depict a stem and leaf plot of the data.
b) Find the mean, median and mode
c) Find the first quartile and the third quartile
d) Find range, interquartile range, variance, standard deviation and the coefficient of variation
e) Using the data obtained from (a) to (d), construct a box-and-whisker plot.
f) Are data skewed? If so, how?
g) What would you tell a customer who purchases this sort of insurance policy and asks how long the approval process takes?
QUESTION 2
a) The Land and Housing department wants to evaluate the various characteristics of single-family houses in the island. A random sample of 70 houses reveals the following:
Area of house (in square feet), sample mean, X= 1,759; S = 380 ft2
42 houses have essential air conditioning
i) Set up a 99 per confidence interval estimate of the population mean area of the houses.
ii) Set up a 95 per confidence interval estimate of the population proportion of houses that have central air conditioning.
b) A group of inhabitants wants to estimate the mean electric bills for the month of July from single-family homes in a city. Based on studies conducted in other cities, the standard deviation is assumed to be Rs 25. The group wants to estimate the mean bill for July to within ± Rs5 of the true average with 99 percent confidence.
i) What model size is essential?
ii) If 95 percent confidence is desired, what sample size is required?
QUESTION 3
An industrial economist claims that high interest rates discourage capital investment spending by firms. To test this, following data was collected showing capital investment spending (X) at different interest rates (Y):
Y ($ billions) X (%)
25 10
26 8
21 9
15 11
17 11
19 11
27 10
26 9
31 7
36 6
39 6
40 5
Number of observation = 12
∑X = 103 ∑Y = 322 ∑X2 = 935
∑Y2 = 9400 ∑XY = 2579
(a) Discover correlation coefficient between X and Y and comment on the result.
(b) Comment also on the usefulness of correlation coefficients in investigating the relationship between variables.
(c) Find the equation of the least squares regression line presumptuous that CIS is the dependent variable (y) and IR is the independent variable (x).
(d) Plan the scatter diagram and plot the regression line.
(e) Predict the effect on the amount of capital investment spending when interest rate rises from 11 to 12 percent. Give Statement on the likely accuracy of your prediction.