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 17 families from a rural area and finds that they have an average income of $69899 with a standard deviation of $717. He then selects 10 families from a urban area and finds that they have an average income of $66383 with a standard deviation of $983. Perform a hypothesis test using a significance level of 0.10 to help him decide.

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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 17 families from a rural area and finds that they
have an average income of $69899 with a standard
deviation of $717. He then selects 10 families from a
urban area and finds that they have an average income
of $66383 with a standard deviation of $983. Perform a
hypothesis test using a significance level of 0.10 to help
him decide.
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 17 families from a rural area and finds that they have an average income of $69899 with a standard deviation of $717. He then selects 10 families from a urban area and finds that they have an average income of $66383 with a standard deviation of $983. Perform a hypothesis test using a significance level of 0.10 to help him decide.
Expert Solution
Step 1

Given Information : 

A researcher claim that average income of rural families is different that average income of urban families . 

Let, μ1 denotes average income of rural families  & μ2 denotes average income of urban families. 

Notations : 

Sample means : 

Statistics homework question answer, step 1, image 1

Sample Standard deviations : 

Statistics homework question answer, step 1, image 2 

and the sample sizes are and 

To test the claim : 

State the hypothesis : 

Ho:  = 

Ha:  ≠ 

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