Question

Have everyone in class take his or her temperature on a healthy day. Test the claim that the median body temperature is 98.6
F.

Answer 1

We consider the following data of body temperature for 10 students on a healthy day.

99.4, 99.5, 99.7, 97.9, 98.8, 98.3, 98.6, 97.8, 98.9, and 99.1

 

We want to test claim that the median body temperature is 98°F.

 

Step 1: Hypotheses and the claim are shown below.

H0: median = 98.6°F (Claim)

H1: median ≠ 98.6°F

 

Step 2: Critical value.

Compare each value of the data with the median.

 

If the value is greater than the median, replace the value with a plus sign. If it is less than the median, replace it with a minus sign. And if it is equal to the median, replace it with at 0. The completed table follows.

+ + + - +

+ 0 - + +

 

From the critical values of the sign test table, using n = 9 (the total number of plus and minus signs; omit the zeros) and α = 0.05 for a two-tailed test; the critical value is 1.

 

Step 3: Test value.

Count the number of plus and minus signs obtained in step 2, and uses the smaller value as the test value. Since there are 7 plus signs and 2 minus signs, 2 is the test value.

 

Step 4: Decision.

Compare the test value 2 with the critical value 1. If the test value is less than or equal to the critical value, the null hypothesis is rejected. In this case, the null hypothesis is not rejected since 2 > 1.

 

Step 5: Summary.

There is enough evidence to support the claim that the median body temperature is 98.6°F.

There is enough evidence to support the claim that the median body temperature is 98.6°F.