Question

Supplementary Problem 10.71

For the two large newspapers in your city, you are interested in knowing whether there is a significant difference in the average number of pages in each dedicated solely to advertising. You randomly select 10 editions of newspaper A and 6 editions of newspaper B (excluding weekend editions). The data follow. use a = 0.01 to test whether there is a significant difference in averages. Assume the number of pages of advertising per edition is normally distributed and the population variances are approximately equal.

A: 17, 17, 21, 15, 11, 21, 21, 22, 16, 18
B: 6, 14, 11, 9, 10, 6

(Round the intermediate values to 3 decimal places. Round your answer to two decimal places.)

Observed t = _______
The decision is to _________

Answer 1

Answer)

Null hypothesis Ho : u1 = u2

Alternate hypothesis Ha : u1 not equal to u2

First we need to find the sample mean and sample s.d for both the groups

For a

x1 = 17.9

S1 = 3.4464

N1 = 10

For. B

X2 = 9.3

S2 = 3.0767

N2 = 6

When the population variances are equal

Then test statistics is = (x1-x2)/standard error

Where standard error = sp√{(1/n1)+(1/n2)}

Sp = √{(n1-1)*s1^2 + (n2-1)*s2^2 }/√{n1+n2-2}

Observed t = 5.012

Degrees of freedom is = n1+n2-2 = 14

For 14 dof and 5.012 test statistics

P-value from t distribution is = 0.00019

As 0.00019 is less than the given significance 0.01

The decision is to reject the null hypothesis