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# Testing of Hypothesis

Exercise 1
Calculate a four-quarter weighted moving average for the number of America Online (AOL) subscribers for the nine quarters of data. The data are reported in thousands. Apply weights of .1, .2, .3 and .4, respectively, for the quarters. In a few words, describe the trend in the number of subscribers.

31-Mar-01 28,766

30-Jun-01 30,057

30-Sep-01 31,336

31-Dec-01 33, 240

31-Mar-02 34,610

30-Jun-02 35,102

30-Sep-02 35,308

31-Dec-02 35,203

31-Mar-03 34,386

Part II

1. Define:
Statistics
Hypothesis
Parameter

2. In a particular market there are three commercial television stations, each with its own evening news program from 6:00 to 6:30 P.M. According to a report in this morning's local newspaper, a random sample of 150 viewers last night revealed 53 watched the news on WNAE (channel 5), 64 watched on WRRN (channel 11), and 33 on WSPD (channel 13). At the .05 significance level, is there a difference in the proportion of viewers watching the three channels?

3. A rental company charges \$30 a day and 15 cents per mile for renting a car. Let y be the total charges (in dollars) for a car for one day and x be the miles driven. The equation for the relationship between x and y is:
Y = 30 + .15X

How much will a person pay who rents a car one day and drives it 100 miles?
Suppose each of 20 persons rents a car from this agency for one day and drives it 100 miles. Will each of them pay the same amount for renting a car for a day or is each person expected to pay a different amount? Explain.

Is the relationship between X and Y exact or nonexact?

Identify the dependent and independent variables.

#### Solution Preview

Weighted Moving average
Instead of just adding up the measurements for a sequence of quarters and dividing by the number of quarters, in a weighted moving average each measurement is first multiplied by a weight factor which differs from quarter to quarter. The final sum is divided, not by the number of quarters, but by the sum of all the weight factors.

Quarter Month (AOL) subscribers Weight Weighted Moving Average
Q1 31-Mar-01 28,766 0.1
Q2 30-Jun-01 30,057 0.2 31584.8
Q3 30-Sep-01 31,336 0.3 32169.2
Q4 31-Dec-01 33,240 0.4 33178.2
Q1 31-Mar-02 34,610 0.1 34369.8
Q2 30-Jun-02 35,102 0.2 35155.0
Q3 30-Sep-02 35,308 0.3
Q4 31-Dec-02 35,203 0.4
Q1 31-Mar-03 34,386 0.1

(Please note that Weighted averages are to be placed between the Q2&Q3 ,Q3&Q4 etc)
See Excel file for calculation.

Trend in the number of AOL subscribers is illustrated in the graph below.
It can be noted that there is an increasing tendency for the first 7 months . The trend becomes negative towards the end of the given data. The over all tendency can be measured by the slope of the regression line. The estimated regression line is
Subscribers = 29135 + 795.4 * x , where x is the number of quarters since Q1 , 2001.
Thus on the average 795.4 new members join AOL in every quarter.

Part II
Statistics: A statistic is a quantity calculated ...

#### Solution Summary

The solution gives the complete details of regression analysis,time series analysis and Chi square test. Step by step procedure of the calculation is given with interpretations.

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