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 1.2 micrograms/mL, the researcher’s hypothesis, for a level of significance of 1%, should resemble which of the following sets of hypothesis?

Answer 1

H0: <= 3.7

Ha: > 3.7

Test statistics

t = - / (S / sqrt(n) )

= 6.1 - 3.7 / (1.2 / sqrt(93) )

= 19.29

This is test statistics value.

df = n - 1 = 93 - 1 = 92

From T table,

Critical value at 0.01 significance level with 92 df = 2.368

Since test statistics value falls in rejection region, that is greater than 2.368, we have sufficient evidence to

reject H0.

We conclude at 0.01 significance level that we have enough evidence to support the claim.