Solve for the following equation step by step and justify your steps when using an exponential property.
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Answer:
We conclude that seniors skip more than 2% of their classes at 0.01 level of significance.
Step-by-step explanation:
We are given that a professor wishes to discover if seniors skip more classes than freshmen. Suppose he knows that freshmen skip 2% of their classes.
He randomly samples a group of seniors and out of 2521 classes, the group skipped 77.
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<u><em>Let p = percentage of seniors who skip their classes.</em></u>
So, Null Hypothesis, : p
2% {means that seniors skip less than or equal to 2% of their classes}
Alternate Hypothesis, : p > 2% {means that seniors skip more than 2% of their classes}
The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics</u>;
T.S. = ~ N(0,1)
where, = sample proportion of seniors who skipped their classes =
n = sample of classes = 2521
So, <u><em>test statistics</em></u> =
= 3.08
The value of the test statistics is 3.08.
Now at 0.01 significance level, <u>the z table gives critical value of 2.3263 for right-tailed test</u>. Since our test statistics is more than the critical value of z as 2.3263 < 3.08, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.
Therefore, we conclude that seniors skip more than 2% of their classes.