Answer :
To determine the null and alternative hypotheses for this hypothesis test, let's first understand the situation:
What and Why:
You're performing a hypothesis test to determine if the average body temperature of a population differs from the commonly accepted value of 98.6 degrees Fahrenheit. In statistical terms, you're testing if there's a significant difference between the sample mean and the population mean of 98.6°F.
How:
Null Hypothesis (H0): This represents the statement you usually want to test against. It assumes that there is no effect or no difference. For this question, the null hypothesis is that the population mean, [tex]\mu[/tex], is equal to 98.6°F.
[tex]H_0: \mu = 98.6[/tex]
Alternative Hypothesis (Ha): This represents what you want to prove. It is the opposite of the null hypothesis. In this case, you want to see if the population mean is not equal to 98.6°F. This is a two-tailed test because you're checking for any difference (either higher or lower).
[tex]H_a: \mu \neq 98.6[/tex]
Significance Level: You're using a significance level of 0.05. This means you are choosing a 5% risk of concluding that a difference exists when there is no actual difference.
With the above understanding, the correct choice for the hypotheses is:
E. [tex]H_0: \mu = 98.6, \; H_a: \mu \neq 98.6[/tex]
In conducting the test, you would calculate the sample mean and sample standard deviation, and use these to compute a t-statistic. You would then compare this statistic to a critical value from the t-distribution (based on your significance level and degrees of freedom) to determine if you can reject the null hypothesis. If your calculated p-value is less than 0.05, you would reject the null hypothesis, indicating that there is a significant difference in body temperature from the expected mean of 98.6°F.
