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Chapter 8: Problem 81

A community college used enrollment records of all students and reported that that the percentage of the student population identifying as female in 2010 was \(54 \%\) whereas the proportion identifying as female in 2018 was \(52 \%\). Would it be appropriate to use this information for a hypothesis test to determine if the proportion of students identifying as female at this college had declined? Explain.

Short Answer

Expert verified
No, it would not be appropriate to use this information for a hypothesis test to determine if the proportion of students identifying as female at this college had declined. Additional data is needed to avoid a potential statistical error.

Step by step solution

01

Understanding Hypothesis Test

In hypothesis testing, a claim is first made about a population. This claim, which is known as a hypothesis, could be about the percentage of females in a school, the feedback received for a product, etc. The goal of hypothesis testing is to determine the likelihood that a population parameter, such as a mean or proportion, is likely to be true.
02

Assessing the Information

From the problem, it is seen that the percentage of students identifying as female dropped from 54% in 2010 to 52% in 2018.
03

Baseline for Hypothesis Testing

A mere drop in percentage does not provide compelling evidence for a claiming a decline. The proportion change could be due to random chance. In order to perform a hypothesis test, more information such as the total number of students each year is needed to calculate standard errors, confidence intervals etc.
04

Conclusion

With the available information, it would not be appropriate to run a hypothesis test. The dropped percentage alone does not provide sufficient numerical evidence to infer a decline in the proportion of students identifying as female from 2010 to 2018. More data is needed to avoid a type I or type II error while performing a hypothesis test. In summary, hypothesis testing, in this case, cannot be reliably performed without additional data.

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Most popular questions from this chapter

A study is done to see whether a coin is biased. The alternative hypothesis used is two-sided, and the obtained \(z\) -value is 1 . Assuming that the sample size is sufficiently large and that the other conditions are also satisfied, use the Empirical Rule to approximate the p-value.

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