Question

5. One study found that 130 out of 250 patient who used the LAMA drug said their weight could be reduced in a given time. Meanwhile, 128 out of 200 people who use NEW medicine admit that their weight has decreased in a specified time. State the hypothesis that you feel is appropriate to test whether there is a difference in the ability of OLD medicine and NEW medicine in weight loss? Test the hypothesis you have built in (i) at the significance level of 5%.

Answer 1

p₁ = proportion of time OLD medicine reduces weight

p₂ = proportion of time NEW medicine reduces weight

H₀: p₁ = p₂

H₁: p₁ ≠ p₂

Two-sample z-test for sample proportions:

$\hat{p_1} = \frac{130}{250} = 0.52 \\ \hat{p_2} = \frac{128}{200} = 0.64 \\ n_1 = 250 \\ n_2 = 200 \\ SE=\sqrt{p(1-p)(\frac{1}{n_1}+ \frac{1}{n_2}}) \\ = 0.04692 \\ z = \frac{\hat{p_1} -\hat{p_2}}{SE} \\ = -2.557$

p-value $= P(Z≤-2.557) \times 2 = 0.0105$

p-value < 0.05

So, we reject the null hypotheses.

There is evidence that the ability of OLD and NEW medicine differ.