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Suppose that we wish to test Ho: p = 0.5 agaisnt Ha: p> 0.5 where p is the probability that a particular coin comes up heads. The plan is to toss the coin 4 times and reject the null hypothesis if all 4 coins come up heads. (a) Determine the probability of a Type I error here. Use exact calculations with the binomial distribution (i.e. do not use a large-sample z-test). (b) If p = 0.75, what is the probability of making a Type II error? (c) Suppose that the coin truly is unbiased (so p= 0.5) and the coin tossing experiment results in three heads followed by a tail. Will you make a Type I error, a Type II error, or no error?

Suppose that we wish to test Ho: p = 0.5 agaisnt Ha: p> 0.5 where p is the probability that a particular coin comes up heads. The plan is to toss the coin 4 times and reject the null hypothesis if all 4 coins come up heads. (a) Determine the probability of a Type I error here. Use exact calculations with the binomial distribution (i.e. do not use a large-sample z-test). (b) If p = 0.75, what is the probability of making a Type II error? (c) Suppose that the coin truly is unbiased (so p= 0.5) and the coin tossing experiment results in three heads followed by a tail. Will you make a Type I error, a Type II error, or no error?

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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Suppose that we wish to test Ho: p = 0.5 agaisnt Ha: p> 0.5 where p is the probability that a particular coin comes up heads. The plan is to toss the coin 4 times and reject the null hypothesis if all 4 coins come up heads. (a) Determine the probability of a Type I error here. Use exact calculations with the binomial distribution (i.e. do not use a large-sample z-test). (b) If p = 0.75, what is the probability of making a Type II error? (c) Suppose that the coin truly is unbiased (so p = 0.5) and the coin tossing experiment results in three heads followed by a tail. Will you make a Type I error, a Type II error, or no error?
Transcribed Image Text:Suppose that we wish to test Ho: p = 0.5 agaisnt Ha: p> 0.5 where p is the probability that a particular coin comes up heads. The plan is to toss the coin 4 times and reject the null hypothesis if all 4 coins come up heads. (a) Determine the probability of a Type I error here. Use exact calculations with the binomial distribution (i.e. do not use a large-sample z-test). (b) If p = 0.75, what is the probability of making a Type II error? (c) Suppose that the coin truly is unbiased (so p = 0.5) and the coin tossing experiment results in three heads followed by a tail. Will you make a Type I error, a Type II error, or no error?
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