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Question: a researcher is evaluating a hypothesis for americans living in...

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A researcher is evaluating a hypothesis for Americans living in rural regions of the United States: that the mean income among black Americans is lower than among white Americans. According to existing research data, white Americans in rural regions have a mean income of 

44,685. The researcher conducted a simple random sample of 202 black heads-of-households in rural regions and found that their mean income was 40,896 (standard deviation=10,861.77).

 

The researcher conducted a one-proportion z-test, with an α-level of 0.05. She declared the hypotheses...

H0 : p = 44,685

HA : p < 44,685

...and, after calculating a z-test statistic, found a p-value < 0.001. What was the probability of the researcher committing a type I error?

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