Question

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method.

A simple random sample of 55 adults is obtained from a normally distributed population, and each person’s red blood cell count (in cells per microliter) is measured. The sample mean is 5.26 and the sample standard deviation is 0.54. Use α = .07 to test the claim that the sample is from a population with µ < 5.4, where 5.4 represents the maximum usual value of a person’s red blood cell count. What does the final conclusion suggest about the sample group?

Answer 1

H0: = 5.4

Ha: < 5.4

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 5.26 - 5.4 ) / ( 0.54 / √(55) )
t = -1.92

Decision based on P value
P - value = P ( t > 1.9227 ) = 0.0299 (From T table)
Reject null hypothesis if P value < α = 0.07 level of significance
P - value = 0.0299 < 0.07 ,hence we reject null hypothesis

Conclusion :- We have sufficient evidence to support the claim that true mean value of the

person’s red blood cell count is less than 5.4 .