Answer :
Final answer:
The hypothesis that the population mean is not 98.6°F is tested using a one-sample t-test. The calculated t-value is compared to the critical t-value at a significance level of 0.05 to determine whether to reject or fail to reject the null hypothesis.
Explanation:
To test the hypothesis that the population mean is not 98.6°F, we will use a one-sample t-test. The null hypothesis, denoted as H0, assumes that the population mean is 98.6°F. The alternative hypothesis, denoted as H1, assumes that the population mean is not 98.6°F.
First, we calculate the sample mean and standard deviation from the given data. The sample mean is the average of the body temperatures: (98.5 + 98.2 + 99.0 + 96.3 + 98.3 + 98.7 + 97.2 + 99.1 + 98.7 + 97.2) / 10 = 98.6°F. The sample standard deviation is a measure of the variability in the data.
Next, we calculate the test statistic, which is the t-value. The formula for the t-value is:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
Substituting the values, we get:
t = (98.6 - 98.6) / (sample standard deviation / sqrt(10))
Since the sample mean is equal to the hypothesized mean, the numerator becomes 0. The denominator is the standard error of the mean, which is the sample standard deviation divided by the square root of the sample size.
Finally, we compare the calculated t-value to the critical t-value at the given significance level (0.05). If the calculated t-value falls within the critical region, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Learn more about hypothesis testing here:
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