A telecommunications company provided its cable TV subscribers with free access

Question

A telecommunications company provided its cable TV subscribers with free access to a new sports channel for a period of one month. It then chose a simple random sample of 400 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 25 of the 400 replied that they would be willing to pay. The marketing director of the company claims that at least 5% of all its subscribers would pay for the channel. Can you conclude that the director's claim is true? Use the a = 0.01 level of significance. Claim in symbolic form: Opposite in symbolic form: H_o in symbolic: H_1 in symbolic form: Which curve is appropriate? (circle one) z t Degrees of freedom (if not applicable, write NONE on the blank) df = What is the tail structure of the test? (circle one) left right two What is (are) the critical value(s)? What is the value of the test statistic? What is the P-value? What is your initial conclusion? (circle one) Reject the Ho Fail to Reject the H_o Write a complete sentence wording your conclusion (no symbols): P-Value Sketch:

Explanation / Answer

Answers:

Claim in symbolic form: p 0.05

Opposite in symbolic form: p < 0.05

H0 in symbolic: H0: p 0.05

H1 in symbolic form: H1: p < 0.05

The Z curve is appropriate.

None degrees of freedom

Left tailed test

Critical value: -2.3263

Test statistic formula is given as below:

Z = (P – p) / sqrt(pq/n)

Where, P is the sample proportion, p is the population proportion, q = 1 – p = 1 – 0.05 = 0.95

And n is the sample size

We are given X = number of favourable items = 25, n = 400, so P = 25/400 = 0.0625, p = 0.05

Plug all values in the above formula

Z = (0.0625 – 0.05)/sqrt(0.05*0.95/400)

Z = 1.1471

Test statistic value = Z = 1.1471

P-value = 0.8743

Conclusion: Fail to reject the H0

Conclusion in words:

There is sufficient evidence to conclude that at least 5% of all subscribers would pay for the channel.

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