Question

Complaints concerning excessive commercials seem to grow as the amount of “clutter,” including commercials and advertisements for other television shows, steadily increases on network and cable television. A recent analysis by Nielsen Monitor-Plus compares the average nonprogram minutes in an hour of prime time for both network and cable television. Data for selected years are shown as follows. Year 1996 1999 2001 2004 Network 9.88 14.00 14.65 15.80 Cable 12.77 13.88 14.50 14.92 a. Calculate the correlation coefficient for the average nonprogram minutes in an hour of prime time between network and cable television. b. Conduct a hypothesis test to determine if a positive correlation exists between the average nonprogram minutes in an hour of prime time between network and cable television. Use a significance level of 0.05 and assume that these figures form a random sample.

Answer 1

Solution

a) Calculation for determining correlation value:

Let X be the average nonprogram minutes in an hour of prime time for network

Let Y be the average nonprogram minutes in an hour of prime time for cable

b) Testing the significance of the correlation coefficient

In this case, number of data point n = 4

Degrees of Freedom df = n - 2

df = 4 - 2 = 2

Computed r = 0.9788

Using the 95 Percent Critical Values of the Sample Correlation Coefficient Table with df = 2, we find that the critical value is 0.950 (Screen shot attached). This means the critical values are really ±0.632. Since r = .9788 and .9788 > 0.950, r is significant.

Thus, we can say that correlation between the average nonprogram minutes in an hour of prime time between network and cable television is positive and significant.