Question

A set of researchers believed that the normal body temperature of children is actually more than 98.6 degrees while sleeping. They measured the temperature in 15 randomly selected healthy adolescents and found a sample mean of 98.9 degrees with a standard deviation of 0.6 degrees with the temperatures being normally distributed. Use a t critical value of 2.14

a. Write the null and alternate hypothesis.

b. Calculate the test statistic and write a conclusion for this question.

c. Now suppose a sample of 150 adolescents was taken and the same mean (98.9) and standard deviation (.6) was achieved. Repeat the test and write a new conclusion. Use a t critical value of +/- 1.98

d. Explain what caused the difference between the conclusions for parts b and c.

Answer 1

a) NULL HYPOTHESIS H0: Degrees

ALTERNATIVE HYPOTHESIS Ha: Degrees

b) Test statistic under null hypothesis H0 is

t critical (given)= 2.14

Since t critical GREATER THAN t calculated therefore DO NOT REJECT H0.

Conclusion: We don't have sufficient evidence to conclude that the normal body temperature of children is actually more than 98.6 degrees while sleeping.

c) Now for n=150 we have same mean (98.9) and standard deviation (.6)

t critical = 1.98 (Given)

Since t critical SMALLER THAN t calculated therefore REJECT H0.

Conclusion: We have sufficient evidence to conclude that the normal body temperature of children is actually more than 98.6 degrees while sleeping.

d) The sample size in second test is 10 times larger than the sample size used in first test. So increased sample size caused the difference between the conclusions for parts b and c.