Question

A telecommunications company provided its cable TV subscribers with free access to a new sports channel for a period of 1 month. It then chose a sample of 398 television viewers and asked them whether they would be willing to pay an extra $10 per month to continue to access the channel. A total of 27 of the 398 replied that they would be willing to pay. The marketing director of the company claims that the percentage of all of its subscribers who would pay for the channel differs from 8%. Can you conclude that the director's claim is true? Use the α=0.10 level of significance and the P-value method with the table.

a. State the appropriate null and alternate hypotheses

b. Compute the value of the test statistic.

c. Using α=0.10, can you conclude that the director's claim is true?

d. state a conclusion

Answer 1

Solution :

Given that,

= 0.08

1 - = 0.92

n = 398

x = 27

Level of significance = = 0.10

Point estimate = sample proportion = = x / n = 0.068

a)

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.08

Ha: p 0.08

b)

Test statistics

z = ( - ) / *(1-) / n

= ( 0.068 - 0.08) / (0.08*0.092) /398

= -0.882

P-value = 2 * P(Z < z )

= 2 * P(Z < -0.882 )

= 2 * 0.1889

= 0.3778

c)

The p-value is p = 0.3778, and since p = 0.3778 > 0.10, it is concluded that fail to reject the null hypothesis.

d)

There is not sufficient evidence to claim that the percentage of all of its subscribers who would pay for the channel differs from 8%.