Data Set 2 in Statdisk (Body temp) includes a sample of 106 body temperatures with a
mean of 98.20 F. Assume that σ is known to be 0.62F. Consider a hypothesis test that
uses a 0.05 significance level to test the claim that the mena body temperature of the
population is less than 98.6F.
What
What
What
What
is the test statistic?
is the critical value?
is the P-value?
is the conclusion about the null hypothesis (reject, fail to reject)?
Answer
Let X be the body temperature and µ be the mean body temperature of the population.
The null hypothesis tested here is
H 0 : µ = 98.6
H 1: µ < 98.6
What is the test statistic?
The test statistic used is
X −µ
Z=
~ N (0,1) = -6.6423
σ/ n
What is the critical value?
Critical value = 1.6449
What is the P-value?
P value = 0.0000
What is the conclusion about the null hypothesis (reject, fail to reject)?
Since calculated value is less than the critical value, we reject the null hypothesis
2
Using results listed in Data Set 5 in Statdisk (Chmovie), test the claim that the majority of
animated children’s movies show the use of alcohol or tobacco (or both). Use a 0.05
significance level.
Answer
Out of the 50 movies 34 show the use of alcohol or tobacco (or both). Thus the sample
proportion is 34 /50 = 0.68
Thus null hypothesis tested is
H 0 : p = 0.5
H 1: p > 0.5
Conclusion: Since the test statistic is greater than the critical value , we reject the null
hypothesis
3
Use the weights of the post 1964 quarters listed in Statdisk (Coin Weights). Test the
claim that the quarters are manufactured according to the U.S. mint specifications that the
mean is equal to 5.670g.
The null hypothesis tested here
H 0 : µ = 5.670
H 1: µ ≠ 5.670
Conclusion : Since the test statistic is greater than the critical value, we reject the null
hypothesis.