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Answer:
We conclude that 18% of all high school students smoke at least one pack of cigarettes a day.
Step-by-step explanation:
We are given that researchers suspect that 18% of all high school students smoke at least one pack of cigarettes a day.
At the local high school, a randomly selected sample of 300 students found that 50 students smoked at least one pack of cigarettes a day.
Let p = <u><em>proportion of all high school students who smoke at least one pack of cigarettes a day.</em></u>
So, Null Hypothesis, : p = 18% {means that 18% of all high school students smoke at least one pack of cigarettes a day}
Alternate Hypothesis, : p < 18% {means that less than 18% of all high school students smoke at least one pack of cigarettes a day}
The test statistics that would be used here is <u>One-sample z -test for proportions</u> because we are given with the proportions values;
T.S. = ~ N(0,1)
where, = sample proportion of students who smoked at least one pack of cigarettes a day =
= 0.167
n = sample of students = 300
So, <u><em>test statistics</em></u> =
= -0.604
The value of z test statistics is -0.604.
Also, P-value of the test statistics is given to us is 0.2743.
Since, the P-value of test statistics is more than the level of significance as 0.2743 > 0.025, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.
Therefore, we conclude that 18% of all high school students smoke at least one pack of cigarettes a day.