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Hypothesis Testing & Confidence

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Question 1: Hypothesis testing allows you to verify whether a supposition is correct. By considering the variables, you may also be able to analyze the reason why the hypothesis is proven correct or incorrect.

Describe in your own words the differences between type I and type II errors. In addition to your explanation, you may submit examples from your experiences which illustrate the differences.

Question 2: Confidence

Note: You are not provided all the information needed in this scenario. Discover what information is missing and state why you need it to make an honest estimation of the results. Then take your best guess as to the race results.

Candidates for election are often compared by the television commentators as winning or losing a recent poll or survey by a "plus or minus margin of error."

Let's say that Candidate Q is announced as ahead in the race by 49% with a plus or minus margin error of 2 percentage points. The other candidate, Candidate Z, was shown to have 47% of the survey results with the same margin for error.

In another survey taken the same day in a different location, Candidate Z is shown as leading by 49% over Candidate Q, who has polled only 46% with a 3 percentage point margin of error.

Based on what you know about confidence intervals, which candidate do you believe is ahead in the race based on these results? Explain.

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Question 1: Solution: A type I error occurs if the null hypothesis is rejected when it is true; A type II error occurs if the null hypothesis is not rejected when it is false. For instance, if we test

Null hypothesis Ho: The mean amount of money spent per month by adults is $500.

1) We conclude that ...

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Based on data from USA Today, tax returns include an option of designating $3 for presidential election campaigns, and it does not cots the taxpayer anything to make that designation. In a simple random sample of 250 taxpayer returns from 1976, 27.6% of the returns designated the $3 for the campaign. In a simple random of 300 recent returns, 7.3% of the returns designated the $3 for the campaign.
Construct a 98% confidence interval estimate for the difference of the percentages of returns designating the $3 for the campaign in 1976 and that of the recent returns. What conclusion does the confidence interval suggest?

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