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Hypotheses Testing Error Types

QUESTION 1
A study conducted in March 2009 found that about half of U. S. adults trusted the U. S. government more than U. S. business to solve the economic problems of the United States. However, when the population is subdivided by political party affiliation, the results are very different. The study showed that 72% of Democrats trusted the government more, but only 29% of Republicans trusted the government more. Suppose that you are in charge of updating the study. You will take a national sample of Democrats and a national sample of Republicans and then try to use the results to show statistical evidence that the proportion of Democrats trusting the government more than business is greater than the proportion of Republicans trusting the government more than business.

a. What are the null and alternative hypotheses?
b. What is a Type I error in the context of this study?
c. What is a Type II error in the context of this study?
Also,
(D) TEST THE HYPOTHESES. DECIDE ON THE IN APPROPRIATE ALPHA

QUESTION 2

According to a poll the mean number of cell phone calls per month was 290 for 18 to 24 year olds and 194 for 45 to 54 year olds, where as the mean number of text messages per month was 290 for 18 to 24 year olds and 57 for 45 to 54 year olds. Suppose that the poll was based on a sample of 100 18 to 24 year olds and 100 45 to 54 year olds and that the standard deviation of the number of cell phone calls per month was 100 for 18 to 24 year olds and 90 for 45 to 54 year olds, where as the standard deviation of the number of text messages per month was 90 for 18 18 to 24 years olds and 77 for 45 to 54 year olds.

Using a level of significance of .05
A) IGNORE
B) is ther evidence of a difference in the mean number of cell phone calls per month for 18 to 24 year olds and for 45 to 54 year olds

C)Construct and interpret a 95% confidence interval estimate for the difference in the mean number of cell phone calls per month for 18 to 24 year olds and 45 to 54 year olds
D)IGNORE
E) Is there evidence of a difference in the mean number of text messages per month for 18 to 24 year olds and 45 to 54 year olds

F) Construct and interpret a 95% confidence interval estimate for the difference in the mean number of text messages per month for 18 to 24 year olds and 45 to 54 year olds

G) Based on the results of (A) THROUGH (F) what conclusions can you make concerning cell phone and text message usage between 18 to 24 year olds and 45 to 54 year olds

Solution Preview

Hypotheses testing
QUESTION 1
A study conducted in March 2009 found that about half of U. S. adults trusted the U. S. government more than U. S. business to solve the economic problems of the United States. However, when the population is subdivided by political party affiliation, the results are very different. The study showed that 72% of Democrats trusted the government more, but only 29% of Republicans trusted the government more. Suppose that you are in charge of updating the study. You will take a national sample of Democrats and a national sample of Republicans and then try to use the results to show statistical evidence that the proportion of Democrats trusting the government more than business is greater than the proportion of Republicans trusting the government more than business.
a. What are the null and alternative hypotheses?
The null hypothesis tested is
H0: The proportion of Democrats trusting the government more than business is NOT greater than the proportion of Republicans trusting the government more than business (P1 ≤ P2).
The alternative hypothesis is
H1: The proportion of Democrats trusting the government more than business is greater than the proportion of Republicans trusting the government more than business (P1 > P2).
b. What is a Type I error in the context of this study?
Type I error, also known as an "error of the first kind", an α error, or a "false positive": the error of rejecting a null hypothesis when it is actually true.
In this context, type I error is the event of concluding that the proportion of Democrats trusting the government more than business is GREATER than the proportion of Republicans trusting the government more than business, when actually there is no significant difference between the two proportions.
c. What is a Type II error in the context of this study?
Type II error, also known as an "error of the second kind", a β error, or a "false negative": the error of not rejecting a null hypothesis when the alternative hypothesis is the true state of nature
In this context, type II error is the event of concluding that the ...

Solution Summary

Hypothesis testing error types are examined.

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