The average body temperature of a healthy adult is 98.6 degrees Fahrenheit. Jenny is concerned that her temperature is elevated, so she took her temperature on 5 randomly chosen occasions. Her average temperature was 99.3 degrees Fahrenheit. Let [tex]x[/tex] be a random variable that represents Jenny's body temperature. You may assume that [tex]x[/tex] has a normal distribution with a standard deviation [tex]\sigma = 0.73[/tex]. Test at the 1% significance level whether Jenny's temperature is significantly different from the average healthy adult temperature.

To test whether Jenny's body temperature is elevated, we can perform a hypothesis test using a t-test. By comparing the calculated t-value to the critical value at a 1% significance level, we can determine whether Jenny's average temperature is elevated or not.

Explanation:

To test whether Jenny's body temperature is elevated, we can perform a hypothesis test. Let's set up the hypotheses:

Null hypothesis (H0): Jenny's average temperature is not elevated and is equal to the average body temperature of a healthy adult, which is 98.6°F.
Alternative hypothesis (Ha): Jenny's average temperature is elevated and is not equal to 98.6°F.

We can use a t-test to test these hypotheses. With a sample mean of 99.3°F and a standard deviation of 0.73°F, we can calculate the t-value and compare it to the critical value at a 1% significance level.

If the t-value is greater than the critical value, we reject the null hypothesis and conclude that Jenny's average temperature is indeed elevated. If the t-value is less than or equal to the critical value, we fail to reject the null hypothesis.

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