Question

Investigators in a clinical study were interested in the impact of lonafarnib, an enzyme inhibitor, on progeria. They recorded PWV, a measure of vascular stiffness, in an SRS of 60 children diagnosed with progeria. All 60 children received a daily dose of lonafarnib for two years, then PWV was assessed once more for each child. What are the correct hypotheses to test the claim that lonafarnib lowers PWV, on average, in children with progeria?

UB= the mean PWV level before treatment with lonafarnib
UA= the mean PWV level after treatment with lonafarnib
Ud= the mean difference in PWV level calculated as Before - After

Answer 1

Null Hypothesis,
`H_0` :
`\mu_B \leq \mu_A` or
`\mu_d \leq 0`

Alternate Hypothesis,
`H_A` :
`\mu_B > \mu_A` or
`\mu_d` > 0

Explanation:

We are given that investigators in a clinical study were interested in the impact of lonafarnib, an enzyme inhibitor, on progeria.

They recorded PWV, a measure of vascular stiffness, in an SRS of 60 children diagnosed with progeria. All 60 children received a daily dose of lonafarnib for two years, then PWV was assessed once more for each child.

The above situation suggests that this is situation of Paired data {Dependent limits} hypothesis because as we can see that the 60 children who received a daily dose of lonafarnib for two years and then the children who were assesses one more time are the same; there are no two independent samples.

This means that both situations are taken from the same sample; there are not any independent samples.

So, the correct hypothesis that would be used here is;

Null Hypothesis,
`H_0` :
`\mu_B \leq \mu_A` or
`\mu_d \leq 0` {means that lonafarnib increases PWV or remains same, on average, in children with progeria}

Alternate Hypothesis,
`H_A` :
`\mu_B > \mu_A` or
`\mu_d` > 0 {means that lonafarnib lowers PWV, on average, in children with progeria}

Here,
`\mu_A` = the mean PWV level after treatment with lonafarnib

`\mu_B` = the mean PWV level before treatment with lonafarnib

`\mu_d` = the mean difference in PWV level calculated as Before - After