Final answer:
To test whether the average human body temperature is different from 37°C, a hypothesis test at the 5% significance level is performed, involving stating the null and alternative hypotheses, calculating the test statistic, and comparing it with the critical z-value to make a decision.
Step-by-step explanation:
Hypothesis Testing for Mean Body Temperature
To determine whether the mean body temperature is different from 37°C, a hypothesis test at the 5% significance level can be used. The null hypothesis (H0) is that the mean body temperature is 37°C, while the alternative hypothesis (H1) is that the mean is different from 37°C.
Here are the steps for the hypothesis test:
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- State the hypotheses: H0: μmu = 37, H1: μmu ≠ 37.
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- Choose the significance level (α): 0.05 in this case.
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- Calculate the test statistic using the formula z = (x8 - μmu)/(sigma/√n), where x8 is the sample mean, μmu is the population mean, sigma is the population standard deviation, and n is the sample size.
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- Determine the critical z-value from the z-table corresponding to the 5% significance level.
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- Compare the test statistic to the critical value. If the test statistic lies outside the range set by the critical values, reject H0.
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- Interpret the results in the context of the study.
>Assumptions for the test include that the sample is randomly selected and that the standard deviation given is a good estimate of the population standard deviation. Also, the central limit theorem supports using the z-distribution when the sample size is small and the population standard deviation is known.