Assignment
The CEO of an insurance institute wants to compare the yearly cost of auto insurance offered by two leading companies. He selects a sample of 20 families, some with only a single insured driver, others with several teenagers, and pays these families a stipend to contact the two companies and ask for a price quote. To make the data comparable, certain features such as the amount deductible are standardised. The sample information is reported below.
Note: Do not change the data into dollars but keep as shown in thousands of dollars.
Insurance Company A |
Insurance Company B |
2.09 |
1.96 |
1.68 |
1.45 |
1.83 |
1.32 |
1.40 |
1.31 |
0.93 |
1.77 |
0.69 |
0.98 |
1.74 |
1.32 |
1.13 |
2.34 |
1.02 |
2.33 |
1.88 |
2.00 |
1.57 |
1.56 |
1.02 |
1.67 |
1.57 |
1.82 |
1.62 |
1.86 |
0.93 |
0.95 |
0.86 |
0.98 |
0.79 |
1.21 |
0.78 |
1.34 |
1.12 |
1.21 |
0.34 |
0.31 |
Table 1: Yearly Cost of Auto Insurance (in $000’s)
Open an Excel spread sheet (you may use Excel 2003, Excel 2007 or Excel 2010) and enter the data which is shown above. The data now represents costs for 20 families. For simplicity we will now refer to ‘Insurance Company A’ as ‘A’ and ‘Insurance Company B’ as ‘B’.
Question 1: 2 marks
a)Use fx to find the standard deviation and modes for the ‘A’ data. Write down the name of the function to verify that you used Excel.
b)Show a table that displays all the summary statistics for the ‘B’ data and highlight the values for the mean, standard deviation and standard error. What is the standard error? Calculate the standard error manually to verify Excel’s result.
Question 2: 2 marks
a)Display a histogram for the ‘B’ data using class widths of 0.25. Describe the shape of the distribution in terms of skewness and kurtosis. What are the values for the skew and for the kurtosis?
b)Display an ogive* for the ‘B’ data and estimate the proportion of costs that exceed 1.5 thousands of dollars.
*When copying your Excel output to ‘word’ include the ‘bin-frequency- cumulative % table.
Question 3: 2 marks
Use an appropriate function on ¦x to estimate the population mean amount for ‘B’ with 95% confidence. Copy onto your word document the formula shown in the formula toolbar. Excel returns (gives you) a single value. Explain what the value refers to. Use this value to manually complete the interval estimate and thus verify the value Excel gave. Interpret the estimate.
Question 4: 1 mark
On a survey an open-ended question asked ‘Of the following five insurance companies which one would you prefer to deal with?’ Five families chose Ace Insurance, three chose Cosmic Insurance, six chose AIG Asia Pacific Insurance, four chose Direct Asia Insurance and two chose Global Health Asia Limited. Show two different ways of displaying this information to best advantage (neither of these displays must be a frequency distribution table).
Question 5: 1 mark
The insurance cost for ‘A’ is normally distributed with a mean of 1.12 thousands of dollars and a standard deviation of 0.8 thousands of dollars. What is the probability that an insurance cost is between 0.82 and 2.13 thousands of dollars? Use an appropriate Excel function (¦x) to determine the probability. Write down the formula shownin the formula bar.
Question 6: 2 marks
Using a = 0.10 determine if there is a difference in the amounts quoted by the two Insurance Companies, A and B. Highlight the relevant critical value or p-value and the test statistic to aid you in interpreting the data.
Subject | Business |
Due By (Pacific Time) | 08/12/2013 04:30 pm |
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