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Answer :
Final answer:
We perform a one-sided lower tail Z-test for the hypothesized population mean body temperature. By comparing the observed Z value with the critical value, we then decide to accept or reject the null hypothesis that the population mean body temperature equals 98.6°F.
Explanation:
To answer the student's question, we need to perform a hypothesis test for the population mean.
In this case, we state our null hypothesis H0 as: the population mean body temperature is 98.6°F. On the other hand, our alternative hypothesis H1 is: the population mean body temperature is less than 98.6°F.
The sample mean is 98.3°F and sample standard deviation is 0.62°F, obtained from a simple random sample of a diverse population of 37 people. Now, we perform a negative Z-test since the hypothesized population mean is higher than the sample mean.
Then, compare the observed (calculated) value of Z with the standard normal distribution values at 0.5% or 0.005 level (which equals to -2.575 for a one-sided test), to make a decision.
If the observed Z value is greater than -2.575, we fail to reject the null hypothesis; this implies the data isn't enough to prove that the population mean body temperature is less than 98.6°F. However, if the observed value is less than -2.575, we reject the null hypothesis; this suggests the population mean is indeed less than 98.6°F .
Learn more about Hypothesis Testing here:
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