Answer:
(a) The proportion of people using nicotine gum that stopped smoking is 0.12 and the proportion of people using the placebo that stopped smoking is 0.05.
(b) The value of z test statistics is 7.242.
Step-by-step explanation:
We are given that a study used nicotine gum to help people quit smoking. The study was placebo-controlled, randomized, and double-blind.
The results showed that 197 out of 1647 people using the nicotine gum succeeded, and 85 out of 1620 using the placebo succeeded.
Let
= <u><em>population proportion of people who quit smoking using nicotine gum.</em></u>
= <u><em>population proportion of people who quit smoking using placebo.</em></u>
SO, Null Hypothesis,
:
Alternate Hypothesis,
:
The test statistics that would be used here <u>Two-sample z test for</u> <u>proportions</u>;
T.S. =
~ N(0,1)
where,
= sample proportion of people using nicotine gum that stopped smoking =
= 0.12
= sample proportion of people using placebo that stopped smoking =
= 0.05
= sample of people using the nicotine gum = 1647
= sample of people using the placebo = 1620
So, <u><em>the test statistics</em></u> = ![\frac{(0.12-0.05)-(0)}{\sqrt{\frac{0.12(1-0.12)}{1647}+\frac{0.05(1-0.05)}{1620} } }](https://tex.z-dn.net/?f=%5Cfrac%7B%280.12-0.05%29-%280%29%7D%7B%5Csqrt%7B%5Cfrac%7B0.12%281-0.12%29%7D%7B1647%7D%2B%5Cfrac%7B0.05%281-0.05%29%7D%7B1620%7D%20%7D%20%7D)
= 7.242
The value of z test statistics is 7.242.