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(c) What is the probability distribution of the test statistic X vhen H, is true? O hypergeometric distribution O Poisson distribution O binomial distribution gamma distribution O normal distribution Use it to compute the P-value when x = 6. (Round your ansver to three decimal places.) 0.0004 (d) If H, is to be rejected when P-value s 0.044, compute the probability of a type 1l error vhen p = 0.4, again when p = 0.3, and also when p = 0.6 and p = 0.7. [Hint: P-value > 0.044 is equivalent to vhat inequalities involving x? Keep in mind that P(type II error when p = 0.4) = P(H, is not rejected when p = 0.4).] (Round your answers to three decimal places.) p- 0.4 0.8406 |x p = 0.3 0.5081 0.8400 0.5061 p= 0.6 p = 0.7

(c) What is the probability distribution of the test statistic X vhen H, is true? O hypergeometric distribution O Poisson distribution O binomial distribution gamma distribution O normal distribution Use it to compute the P-value when x = 6. (Round your ansver to three decimal places.) 0.0004 (d) If H, is to be rejected when P-value s 0.044, compute the probability of a type 1l error vhen p = 0.4, again when p = 0.3, and also when p = 0.6 and p = 0.7. [Hint: P-value > 0.044 is equivalent to vhat inequalities involving x? Keep in mind that P(type II error when p = 0.4) = P(H, is not rejected when p = 0.4).] (Round your answers to three decimal places.) p- 0.4 0.8406 |x p = 0.3 0.5081 0.8400 0.5061 p= 0.6 p = 0.7

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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(c) What is the probability distribution of the test statistic \( X \) when \( H_0 \) is true? - ☐ hypergeometric distribution - ☐ Poisson distribution - ⦿ **binomial distribution** - ☐ gamma distribution - ☐ normal distribution Use it to compute the \( P \)-value when \( x = 6 \). (Round your answer to three decimal places.) 0.0094 ❌ (d) If \( H_0 \) is to be rejected when \( P\text{-value} \leq 0.044 \), compute the probability of a type II error when \( p = 0.4 \), again when \( p = 0.3 \, \) and also when \( p = 0.6 \) and \( p = 0.7 \). [Hint: \( P\text{-value} > 0.044 \) is equivalent to what inequalities involving \( x \)? Keep in mind that \( P(\text{type II error when } p = 0.4) = P(H_0 \text{ is not rejected when } p = 0.4). \)] (Round your answers to three decimal places.) - \( p = 0.4 \) ☐ 0.8496 ❌ - \( p = 0.3 \) ☐ 0.5601 ❌ - \( p = 0.6 \) ☐ 0.8496 ❌ - \( p = 0.7 \) ☐ 0.5061 ❌
Transcribed Image Text:(c) What is the probability distribution of the test statistic \( X \) when \( H_0 \) is true? - ☐ hypergeometric distribution - ☐ Poisson distribution - ⦿ **binomial distribution** - ☐ gamma distribution - ☐ normal distribution Use it to compute the \( P \)-value when \( x = 6 \). (Round your answer to three decimal places.) 0.0094 ❌ (d) If \( H_0 \) is to be rejected when \( P\text{-value} \leq 0.044 \), compute the probability of a type II error when \( p = 0.4 \), again when \( p = 0.3 \, \) and also when \( p = 0.6 \) and \( p = 0.7 \). [Hint: \( P\text{-value} > 0.044 \) is equivalent to what inequalities involving \( x \)? Keep in mind that \( P(\text{type II error when } p = 0.4) = P(H_0 \text{ is not rejected when } p = 0.4). \)] (Round your answers to three decimal places.) - \( p = 0.4 \) ☐ 0.8496 ❌ - \( p = 0.3 \) ☐ 0.5601 ❌ - \( p = 0.6 \) ☐ 0.8496 ❌ - \( p = 0.7 \) ☐ 0.5061 ❌
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 \( H_0 : p = 0.5 \) versus \( H_a : p \neq 0.5 \) 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 \( X \). [There is a button labeled "USE SALT."]
Transcribed Image Text: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 \( H_0 : p = 0.5 \) versus \( H_a : p \neq 0.5 \) 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 \( X \). [There is a button labeled "USE SALT."]
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