Which equation correctly shows the absoulte vaule of -8
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Answer:
We conclude that the proportion of women who smoke cigarettes is smaller than or equal to the proportion of men at 0.01 significance level.
95% confidence interval for the difference in population proportions of women and men who smoke cigarettes is [0.0062 , 0.1298].
Step-by-step explanation:
We are given that random samples of 125 women and 140 men reveal that 13 women and 5 men smoke cigarettes.
<em>Let </em><em> = population proportion of women who smoke cigarettes</em>
<em /><em> = population proportion of men who smoke cigarettes</em>
So, Null Hypothesis, :
{means that the proportion of women who smoke cigarettes is smaller than or equal to the proportion of men}
Alternate Hypothesis, :
{means that the proportion of women who smoke cigarettes is higher than the proportion of men}
The test statistics that will be used here is <u>Two-sample z proportion test</u> <u>statistics</u>;
T.S. = ~ N(0,1)
where, = sample proportion of women who smoke cigarettes=
=0.104
= sample proportion of men who smoke cigarettes =
= 0.036
= sample of women = 125
= sample of men = 140
So, <u><em>the test statistics</em></u> =
= 2.158
Now, at 0.01 significance level, the z table gives critical value of 2.3263 for right tailed test. Since our test statistics is less than the critical value of z as 2.158 < 2.3263, so we have insufficient evidence to reject our null hypothesis due to which <u>we fail to reject our null hypothesis</u>.
Therefore, we conclude that the proportion of women who smoke cigarettes is smaller than or equal to the proportion of men.
<em>Now, coming to 95% confidence interval;</em>
Firstly, the pivotal quantity for 95% confidence interval for the difference between population proportions is given by;
P.Q. = ~ N(0,1)
where, = sample proportion of women who smoke cigarettes=
=0.104
= sample proportion of men who smoke cigarettes =
= 0.036
= sample of women = 125
= sample of men = 140
<em>Here for constructing 95% confidence interval we have used Two-sample z proportion statistics.</em>
<u>So, 95% confidence interval for the difference between population proportions, </u><u> is ;</u>
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u>95% confidence interval for</u> =
[,
]
= [ ,
]
= [0.0062 , 0.1298]
Therefore, 95% confidence interval for the difference in population proportions of women and men who smoke cigarettes is [0.0062 , 0.1298].