A researcher is interested in seeing if the average income of rural families is less than that of urban families. To see if his claim is correct he randomly selects 12 families from a rural area and finds that they have an average income of $69429 with a standard deviation of $554. He then selects 23 families from a urban area and finds that they have an average income of $66936 with a standard deviation of $926. Perform a hypothesis test using a significance level of 0.10 to help him decide. Let the rural families be sample 1 and the urban families be sample 2. The correct hypotheses are: O Ho: µ1 < M2 HA: H1 > µ2(claim) Ο Η: μι > μ2 HA: H1 < µ2(claim) O Ho: H1 = H2 HA: H1 + H2(claim) Since the level of significance is 0.10 critical value is -1.308 The test statistic is: (round to 3 places) The p-value is: (round to 3 places) The decision can be made to: O reject Ho O do not reject Ho The final conclusion is that: O There is enough evidence to reject the claim that the average income of rural families is less than that of urban families. There is not enough evidence to reject the claim that the average income of rural families is less than that of urban families. O There is enough evidence to support the claim that the average income of rural families is less than that of urban families. O There is not enough evidence to support the claim that the average income of rural families is less than that of urban families.
A researcher is interested in seeing if the average income of rural families is less than that of urban families. To see if his claim is correct he randomly selects 12 families from a rural area and finds that they have an average income of $69429 with a standard deviation of $554. He then selects 23 families from a urban area and finds that they have an average income of $66936 with a standard deviation of $926. Perform a hypothesis test using a significance level of 0.10 to help him decide. Let the rural families be sample 1 and the urban families be sample 2. The correct hypotheses are: O Ho: µ1 < M2 HA: H1 > µ2(claim) Ο Η: μι > μ2 HA: H1 < µ2(claim) O Ho: H1 = H2 HA: H1 + H2(claim) Since the level of significance is 0.10 critical value is -1.308 The test statistic is: (round to 3 places) The p-value is: (round to 3 places) The decision can be made to: O reject Ho O do not reject Ho The final conclusion is that: O There is enough evidence to reject the claim that the average income of rural families is less than that of urban families. There is not enough evidence to reject the claim that the average income of rural families is less than that of urban families. O There is enough evidence to support the claim that the average income of rural families is less than that of urban families. O There is not enough evidence to support the claim that the average income of rural families is less than that of urban families.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![A researcher is interested in seeing if the average income of rural families is less than that of urban families. To see if his claim is correct, he randomly selects 12 families from a rural area and finds that they have an average income of $69,429 with a standard deviation of $554. He then selects 23 families from an urban area and finds that they have an average income of $66,936 with a standard deviation of $926. Perform a hypothesis test using a significance level of 0.10 to help him decide.
Let the rural families be sample 1 and the urban families be sample 2.
The correct hypotheses are:
- \( H_0: \mu_1 \le \mu_2 \)
\( H_A: \mu_1 > \mu_2 \) (claim)
- \( H_0: \mu_1 \ge \mu_2 \)
\( H_A: \mu_1 < \mu_2 \) (claim)
- \( H_0: \mu_1 = \mu_2 \)
\( H_A: \mu_1 \neq \mu_2 \) (claim)
Since the level of significance is 0.10, the critical value is -1.308.
- The test statistic is: [__________] (round to 3 places)
- The p-value is: [__________] (round to 3 places)
The decision can be made to:
- \( \bigcirc \) reject \( H_0 \)
- \( \bigcirc \) do not reject \( H_0 \)
The final conclusion is that:
- \( \bigcirc \) There is enough evidence to reject the claim that the average income of rural families is less than that of urban families.
- \( \bigcirc \) There is not enough evidence to reject the claim that the average income of rural families is less than that of urban families.
- \( \bigcirc \) There is enough evidence to support the claim that the average income of rural families is less than that of urban families.
- \( \bigcirc \) There is not enough evidence to support the claim that the average income of rural families is less than that of urban families.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F635fc7d1-4125-4a99-970f-fc3f5300d520%2F6f8c7de3-9035-4f6f-a306-03a1d92cceec%2Fb9fd0b_processed.png&w=3840&q=75)
Transcribed Image Text:A researcher is interested in seeing if the average income of rural families is less than that of urban families. To see if his claim is correct, he randomly selects 12 families from a rural area and finds that they have an average income of $69,429 with a standard deviation of $554. He then selects 23 families from an urban area and finds that they have an average income of $66,936 with a standard deviation of $926. Perform a hypothesis test using a significance level of 0.10 to help him decide.
Let the rural families be sample 1 and the urban families be sample 2.
The correct hypotheses are:
- \( H_0: \mu_1 \le \mu_2 \)
\( H_A: \mu_1 > \mu_2 \) (claim)
- \( H_0: \mu_1 \ge \mu_2 \)
\( H_A: \mu_1 < \mu_2 \) (claim)
- \( H_0: \mu_1 = \mu_2 \)
\( H_A: \mu_1 \neq \mu_2 \) (claim)
Since the level of significance is 0.10, the critical value is -1.308.
- The test statistic is: [__________] (round to 3 places)
- The p-value is: [__________] (round to 3 places)
The decision can be made to:
- \( \bigcirc \) reject \( H_0 \)
- \( \bigcirc \) do not reject \( H_0 \)
The final conclusion is that:
- \( \bigcirc \) There is enough evidence to reject the claim that the average income of rural families is less than that of urban families.
- \( \bigcirc \) There is not enough evidence to reject the claim that the average income of rural families is less than that of urban families.
- \( \bigcirc \) There is enough evidence to support the claim that the average income of rural families is less than that of urban families.
- \( \bigcirc \) There is not enough evidence to support the claim that the average income of rural families is less than that of urban families.
Expert Solution
Step 1
From the given information, the claim of the test is the average income of rural families is less than that of urban families.
The hypotheses are given below:
Null hypothesis:
H0: µ1 ≥ µ2
There is not enough evidence that the average income of rural families is greater than are equal to that of urban families.
Alternative hypothesis:
HA: µ1 < µ2 (claim)
There is enough evidence that the average income of rural families is less than that of urban families.
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