A study used nicotine gum to help people quit smoking. The study was placebo-controlled, randomized, and double-blind. Each participant was interviewed after 28 days, and success was defined as being abstinent from cigarettes for 28 days. The results showed that 197 out of 1647 people using the nicotine gum succeeded, and 85 out of 1620 using the placebo succeeded. Although the sample was not random, the assignment to groups was randomized. a. Find the proportion of people using nicotine gum that stopped smoking and the proportion of people using the placebo that stopped smoking, and compare them. Is this what the researchers had expected? b. Find the observed value of the test statistic, assuming that the conditions for a two-proportion z-test hold.

(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 = population proportion of people who quit smoking using nicotine gum.

= population proportion of people who quit smoking using placebo.

SO, Null Hypothesis, :    

Alternate Hypothesis, :  

The test statistics that would be used here Two-sample z test for proportions;

                        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, the test statistics  =  

                                     =  7.242

The value of z test statistics is 7.242.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)