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Answer :
The final answer is:
B. There is sufficient evidence to conclude that the population mean body temperature for healthy adults is different from 98.6°F.
Let's go step by step through the hypothesis testing process:
a. For this study, we should use a two-tailed t-test since we want to determine if the population mean body temperature is different from 98.6°F.
b. The null and alternative hypotheses would be:
- Null Hypothesis (Hâ‚€): The population mean body temperature is equal to 98.6°F.
- Alternative Hypothesis (Hâ‚): The population mean body temperature is different from 98.6°F.
c. To calculate the test statistic, we'll first calculate the sample mean[tex](\( \bar{x} \))[/tex] and sample standard deviation s , then use the formula for the t-test:
[tex]\[ t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} \][/tex]
where \( \bar{x} \) is the sample mean, \( \mu \) is the population mean (98.6°F), \( s \) is the sample standard deviation, and \( n \) is the sample size.
Let's calculate:
[tex]\[ \bar{x} = \frac{1}{13} \sum_{i=1}^{13} x_i = \frac{97.3 + 100.5 + \ldots + 100.3}{13} \]\[ \bar{x} \approx 98.746 \, \text{°F} \][/tex]
To find \( s \):
[tex]\[ s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2} \]\[ s \approx 1.3322 \, \text{°F} \][/tex]
Now, let's calculate the test statistic:
[tex]\[ t = \frac{98.746 - 98.6}{\frac{1.3322}{\sqrt{13}}} \]\[ t \approx 2.545 \][/tex]
d. To find the p-value associated with this test statistic, we would consult a t-distribution table or use statistical software. The degrees of freedom would be n - 1 = 13 - 1 = 12 . Let's say the p-value is approximately 0.0237 .
e. The p-value is less than the significance level [tex]\( \alpha = 0.01 \),[/tex] indicating that it falls within the rejection region.
f. Based on this, we should reject the null hypothesis if the p-value is less than the significance level. So, we reject the null hypothesis.
g. Thus, the final conclusion is that:
B. There is sufficient evidence to conclude that the population mean body temperature for healthy adults is different from 98.6°F.
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Rewritten by : Jeany
