Question

A researcher is studying the relationship between thyroid hormone levels and smoking. A sample of 100 nonsmokers had a mean hormone level of 120ng/dl with a standard deviation 40ng/dl, while a sample of smokers had a mean hormone level of 110ng/dl with a standard deviation 35ng/dl. A randomly selected individual from the nonsmoking group had a hormone level of 126, while a randomly selected individual from the smoking group had a hormone level of 115. Find the corresponding z-scores. Which individual had a higher hormone level relative to their group (smoking status)?

Q1. What is the non-smoker hormone level? .13 .17 .20 .15

Q2. Did the non-smoker had a hormone level above or below the standard deviation; above or mean the mean?

Q3. The smoker had a hormone level? .14 .16 .12. .19

Q4.The smoker had a hormone level above or below standard deviation; above or below the mean?

Q5. Which individual had a higher hormone level relative to their group? a)The nonsmoker since its z score is smaller, b)the smoker since its z score is larger c) The nonsmoker since its z score is larger d) the smoker since its z score is smaller

Answer 1

1.

For non-smoker,

Z = (x - ) / = (126 - 120) / 40 = 0.15

2.

Since z value is positive, the non-smoker had a hormone level above the mean.

3.

For smoker,

Z = (x - ) / = (115 - 110) / 35 = 0.14

4.

Since z value is positive, the smoker had a hormone level above the mean.

5.

Since z value for nonsmoker is higher than that of smoker, so nonsmoker had a higher hormone level relative to their group.

c) The nonsmoker since its z score is larger