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We conclude that the rate of smoking among those with four years of college is less than the 27% rate for the general population.
Step-by-step explanation:
We are given that a survey showed that among 785 randomly selected subjects who completed four years of college, 144 of them are smokers.
Let p = <u><em>population proportion of smokers among those with four years of college</em></u>
So, Null Hypothesis, : p
27% {means that the rate of smoking among those with four years of college is more than or equal to the 27% rate for the general population}
Alternate Hypothesis, : p < 27% {means that the rate of smoking among those with four years of college is less than the 27% rate for the general population}
The test statistics that will be used here is <u>One-sample z-test</u> for proportions;
T.S. = ~ N(0,1)
where, = sample proportion of smokers =
= 0.18
n = sample of subjects = 785
So, <em><u>the test statistics</u></em> =
= -5.68
The value of z-test statistics is -5.68.
<h2>Also, the P-value of the test statistics is given by;</h2>P-value = P(Z < -5.68) = Less than 0.0001
Now, at a 0.01 level of significance, the z table gives a critical value of -2.3262 for the left-tailed test.
Since the value of our test statistics is less than the critical value of z, so we have <u><em>sufficient evidence to reject our null hypothesis</em></u> as it will fall in the rejection region.
Therefore, we conclude that the rate of smoking among those with four years of college is less than the 27% rate for the general population.