Body Temperatures (Using Table A-2 or StatCrunch) Assume that the population of human body temperatures has a mean of 98.3°F, as is commonly believed. Also assume that the population standard deviation is 0.62°F (based on Data Set 5 “Body Temperatures” in Appendix B). A sample of size
subjects was randomly selected and the mean body temperature of 98.1°F was obtained. If the mean body temperature is really 98.3°F, find the probability of getting a sample mean of 98.1°F or lower for a sample of size 110. Based on the result, is 98.1°F significantly low? What do these results suggest about the common belief that the mean body temperature is 98.3°F? Draw the bell curve. Make sure to label and shade the region. Must include the mean for both the x scale and z scale and include the x and z value in addition to the probability (area). Please see lecture videos. (6 pts)
The Correct Answer and Explanation is:
To solve this, we apply the z-score formula for a sample mean:
Step 1: Given values
- Population mean (μ) = 98.3°F
- Population standard deviation (σ) = 0.62°F
- Sample size (n) = 110
- Sample mean (x̄) = 98.1°F
Step 2: Calculate standard error (SE)
SE=σn=0.62110≈0.6210.4881≈0.0591SE = \frac{\sigma}{\sqrt{n}} = \frac{0.62}{\sqrt{110}} \approx \frac{0.62}{10.4881} \approx 0.0591SE=n
