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Chapter 8, Problem 11E(choose chapter or problem)
Problem 11E
Two different companies have applied to provide cable television service in a certain region. Let p denote the proportion of all potential subscribers who favor the first company over the second. Consider testing Ho: p = .5 versus Ha: p ≠ .5 based on a random sample of 25 individuals. Let the test statistic X be the number in the sample who favor the first company and x represent the observed value of X.
a. Describe type I and II errors in the context of this problem situation.
b. Suppose that x = 6. Which values of X are at least as contradictory to Ho as this one?
c. What is the probability distribution of the test statistic X when Ho is true? Use it to compute the P-value when x = 6.
d. If Ho is to be rejected when P-value≤ .044, compute the probability of a type II error when p = .4, again when p = .3, and also when p = .6 and p = .7. [Hint: P-value > .044 is equivalent to what inequalities involving x (see Example 8.4)?]
e. Using the test procedure of (d), what would you conclude if 6 of the 25 queried favored company 1?
Questions & Answers
QUESTION:
Problem 11E
Two different companies have applied to provide cable television service in a certain region. Let p denote the proportion of all potential subscribers who favor the first company over the second. Consider testing Ho: p = .5 versus Ha: p ≠ .5 based on a random sample of 25 individuals. Let the test statistic X be the number in the sample who favor the first company and x represent the observed value of X.
a. Describe type I and II errors in the context of this problem situation.
b. Suppose that x = 6. Which values of X are at least as contradictory to Ho as this one?
c. What is the probability distribution of the test statistic X when Ho is true? Use it to compute the P-value when x = 6.
d. If Ho is to be rejected when P-value≤ .044, compute the probability of a type II error when p = .4, again when p = .3, and also when p = .6 and p = .7. [Hint: P-value > .044 is equivalent to what inequalities involving x (see Example 8.4)?]
e. Using the test procedure of (d), what would you conclude if 6 of the 25 queried favored company 1?
ANSWER:
Problem 11E
Two different companies have applied to provide cable television service in a certain region. Let p denote the proportion of all potential subscribers who favor the first company over the second. Consider testing Ho: p = .5 versus Ha: p 
a. Describe type I and II errors in the context of this problem situation.
b. Suppose that x = 6. Which values of X are at least as contradictory to Ho as this one?
c. What is the probability distribution of the test statistic X when Ho is true? Use it to compute the P-value when x = 6.
d. If Ho is to be rejected when P-value 
e. Using the test procedure of (d), what would you conclude if 6 of the 25 queried favored company 1?
Step by Step Solution
Step 1 of 8
Let x be the number in the sample that favours the first company over the second.
Let p be the proportion of all potential subscribers who favour the first company over the second.
Let the sample size be n = 25.
The null and alternative hypothesis are
(The proportion of all potential subscribers who favour the first company over the second.)
(The proportion of all potential subscribers who were not favour the first company over the second.)