Question

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 2.4 micrograms/mL, for a level of significance of 1%, what should the researcher’s conclusion be?

		We have significant evidence at the 1% level to reject H0 in favor of H1 because –9.64 is less than –2.576 and determine the mean trough level for the medication to be higher than 3.7 micrograms/mL.
		We have significant evidence at the 1% level to reject H0 in favor of H1 because –9.59 is less than –2.326 and determine the mean trough level for the medication to be higher than 3.7 micrograms/mL.
		We have significant evidence at the 1% level to reject H0 in favor of H1 because 9.64 is greater than 2.326 and determine the mean trough level for the medication to be higher than 3.7 micrograms/mL.
		We have significant evidence at the 1% level to reject H0 in favor of H1 because 9.59 is greater than 2.576 and determine the mean trough level for the medication to be higher than 3.7 micrograms/mL.

Answer 1

The statistical software output for this problem is:

One sample Z summary hypothesis test:
μ : Mean of population
H₀ : μ = 3.7
H_A : μ > 3.7
Standard deviation = 2.4

Hypothesis test results:

Mean	n	Sample Mean	Std. Err.	Z-Stat	P-value
μ	93	6.1	0.24886841	9.6436508	<0.0001

Hence,

We have significant evidence at the 1% level to reject H₀ in favor of H₁ because 9.64 is greater than 2.326 and determine the mean trough level for the medication to be higher than 3.7 micrograms/mL.

Option C is correct.