In: Math
A researcher suspects the mean trough (the lowest dosage of medication required to see clinical improvement of symptoms) level for a medication used to treat arthritis is higher than was previously reported in other studies. If previous studies found the mean trough level of the population to be 3.7 micrograms/mL, and the researcher conducts a study among 93 newly diagnosed arthritis patients and finds the mean trough to be 6.1 micrograms/mL with a standard deviation of 1.2 micrograms/mL, the researcher’s hypothesis, for a level of significance of 1%, should resemble which of the following sets of hypothesis?
Solution :
This is the two tailed test .
The null and alternative hypothesis is ,
H0 : = 3.7
Ha : 3.7
= 6.1
= 3.7
= 1.2
n = 93
Test statistic = z
= ( - ) / / n
= (6.1 - 3.7) / 1.2 / 93
= 19.28
Test statistic = 19.28
P(z > 19.28) = 1 - P(z < 19.28) = 1 - 1 = 0
P-value = 0
= 0.01
P-value <
Reject the null hypothesis .
There is no evidence to the researcher’s hypothesis, for a level of significance of 1%, should not resemble