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?

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 3.7

H_a : > 3.7

= 6.1

= 3.7

= 2.4

n = 93

Test statistic = z

= ( - ) / / n

= (6.1 - 3.7) / 2.4 / 93

= 9.64

Test statistic = 9.64

P(z > 9.64) = 1 - P(z < 9.64) = 1 - 1 = 0

P-value = 0

= 0.01

P-value <

Reject the null hypothesis .

Claim is. true