Answer to Question #146642 in Statistics and Probability for Azlan

Question #146642
We wish to check that normal body temperature may be less than 98.6 degrees. In a random sample of n = 18 individuals, the sample mean was found to be 98.217 and the standard deviation
was 0.684. Assume the population is normally distributed. Use=0.05.
1
Expert's answer
2020-12-02T18:15:57-0500

Population standard deviation is unknown.

H0:μ=98.6H_0:\mu=98.6

Ha:μ<98.6H_a:\mu<98.6

t=Xˉμsnt=\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}

t=98.21798.60.68418t=\frac{98.217-98.6}{\frac{0.684}{\sqrt{18}}}

=2.376=-2.376

t0.05,17=1.74t_{0.05,17}=-1.74

Since the test statistic -2.376 is less than the critical value -1.74, we reject the null hypothesis and conclude that there is enough evidence at 95% confidence level to conclude that normal body temperature is less than 98.6 degrees.


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