A researcher is interested in seeing if the average income of rural families is different than that of urban families. To see if his claim is correct he randomly selects 54 families from a rural area and finds that they have an average income of $67109 with a population standard deviation of $536. He then selects 46 families from a urban area and finds that they have an average income of $67865 with a population standard deviation of $631. Perform a hypothesis test using a significance level of 0.01 to test his claim. Let rural families be sample 1 and urban familis be sample 2.
A researcher is interested in seeing if the average income of rural families is different than that of urban families. To see if his claim is correct he randomly selects 54 families from a rural area and finds that they have an average income of $67109 with a population standard deviation of $536. He then selects 46 families from a urban area and finds that they have an average income of $67865 with a population standard deviation of $631. Perform a hypothesis test using a significance level of 0.01 to test his claim. Let rural families be sample 1 and urban familis be sample 2.
A First Course in Probability (10th Edition)
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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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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![A researcher is interested in seeing if the average income of rural families is different than that of urban families. To see if his claim is correct he randomly selects 54 families from a rural area and finds that they have an average income of $67,109 with a population standard deviation of $536. He then selects 46 families from an urban area and finds that they have an average income of $67,865 with a population standard deviation of $631. Perform a hypothesis test using a significance level of 0.01 to test his claim. Let rural families be sample 1 and urban families be sample 2.
The correct hypotheses are:
- \( H_0: \mu_1 = \mu_2 \)
- \( H_A: \mu_1 \neq \mu_2 \) (claim)
Since the level of significance is 0.01 the critical value is 2.576 and -2.576
The test statistic is: [_______] (round to 3 places)
The p-value is: [_______] (round to 3 places)
The decision can be made to:
- \( \circ \) reject \( H_0 \)
- \( \circ \) do not reject \( H_0 \)
The final conclusion is that:
- \( \circ \) There is enough evidence to reject the claim that the average income of rural families is different than that of urban families.
- \( \circ \) There is not enough evidence to reject the claim that the average income of rural families is different than that of urban families.
- \( \circ \) There is enough evidence to support the claim that the average income of rural families is different than that of urban families.
- \( \circ \) There is not enough evidence to support the claim that the average income of rural families is different than that of urban families.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3906bba-d731-4d3e-8323-fa6146946cae%2Ff3f83aa6-6850-44ae-8d8f-0301a8417c91%2Fv1sfx6ev_processed.png&w=3840&q=75)
Transcribed Image Text:A researcher is interested in seeing if the average income of rural families is different than that of urban families. To see if his claim is correct he randomly selects 54 families from a rural area and finds that they have an average income of $67,109 with a population standard deviation of $536. He then selects 46 families from an urban area and finds that they have an average income of $67,865 with a population standard deviation of $631. Perform a hypothesis test using a significance level of 0.01 to test his claim. Let rural families be sample 1 and urban families be sample 2.
The correct hypotheses are:
- \( H_0: \mu_1 = \mu_2 \)
- \( H_A: \mu_1 \neq \mu_2 \) (claim)
Since the level of significance is 0.01 the critical value is 2.576 and -2.576
The test statistic is: [_______] (round to 3 places)
The p-value is: [_______] (round to 3 places)
The decision can be made to:
- \( \circ \) reject \( H_0 \)
- \( \circ \) do not reject \( H_0 \)
The final conclusion is that:
- \( \circ \) There is enough evidence to reject the claim that the average income of rural families is different than that of urban families.
- \( \circ \) There is not enough evidence to reject the claim that the average income of rural families is different than that of urban families.
- \( \circ \) There is enough evidence to support the claim that the average income of rural families is different than that of urban families.
- \( \circ \) There is not enough evidence to support the claim that the average income of rural families is different than that of urban families.
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