1. Define Hypothesis testing and explain briefly the five standard steps involved in this process.
2. The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes.
Find the probability that a call:
2.1. Lasts between 5 and 10 minutes.
2.2. Lasts more than 7 minutes.
2.3. Lasts less than 4 minutes
3. A manufacturer of light bulbs advertises that, on average, its long-life bulb will last more than 5 000 hours. To test the claim, a statistician took a random sample of
100 bulbs and measured the amount of time each bulb burned out. She found that the sample mean was 5065 hours. If we assume that the lifetime of this type of bulb is normally distributed and has a standard deviation of 400 hours, test at 5% level of
significance the manufacture’s claim is true.
The General Manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month’s sales (in R1 000s) and the years of experience of 10 randomly selected salespeople. These data are listed in the table below:
Table
Salesperson | Year of Experience | Sales |
1 | 0 | 7 |
2 | 2 | 9 |
3 | 10 | 20 |
4 | 3 | 15 |
5 | 8 | 18 |
6 | 5 | 14 |
7 | 12 | 20 |
8 | 7 | 17 |
9 | 20 | 30 |
10 | 15 | 25 |
1.1 | Identify the independent and the dependent variables. | |
1.2 | Construct a scatter plot to portray the data in table 2. | |
1.3 | Calculate the coefficient of correlation. | |
1.4 | Interpret your findings in (2.3) above. | |
1.5 | Use the least-square method to determine the regression equation. | |
1.6 | Explain what the coefficients (the slope and the intercept) of the equation in (2.5) tell you about the relationship between years of experience and monthly sales | |
XXXXXXXXXXEstimate the monthly sales for a salesperson with 16 years of experience.
_{}^{}The prices and per capita consumption of four (4) basic food items for the years 2005 and 2011 are displayed in tablebelow:
Table.
| Prices (R / kg) | Quantities |
Food Item | 2005 | 2011 | 2005 | 2011 |
A | 40 | 56 | 99 | 130 |
B | 56 | 73 | 47 | 50 |
C | 87 | 190 | 23 | 44 |
D | 80 | 91 | 20 | 27 |
1.1 W ith 2005 as base year, calculate for the year 2011 the Laspeyres price and quantity indices and interpret your answers
1.2 The following data refer to the number of visitors (in thousands) that visited the uShaka water world in the years XXXXXXXXXX.
| I Jan-Apr | II May-Aug | III Sep-Dec |
2010 | - | 86 | 98 |
2011 | 84 | 91 | 106 |
2012 | 86 | 104 | 139 |
You are required to:
1.2.1 Obtain a 3-term moving average trend.
1.2.2 Find the seasonal variations using the additive model._{}^{}