Answer:
We conclude that the proportion of dropouts has changed from the historical value of 0.081.
Step-by-step explanation:
We are given that in 2009, the high school dropout rate was 8.1%. A polling company recently took a survey of 1000 people between the ages of 16 and 24 and found 6.5% of them are high school dropouts.
The polling company would like to determine whether the proportion of dropouts has changed from the historical value of 0.081.
<em>Let p = proportion of school dropouts rate</em>
SO, <u>Null Hypothesis,</u> : p = 0.081 {means that the proportion of dropouts has not changed from the historical value of 0.081}
<u>Alternate Hypothesis</u>, : p
0.081 {means that the proportion of dropouts has changed from the historical value of 0.081}
The test statistics that will be used here is <u>One-sample z proportion statistics</u>;
T.S. = ~ N(0,1)
where, = sample proportion of high school dropout rate = 6.5%
n = sample of people = 1000
So, <u><em>test statistics</em></u> =
= -2.05
<u>Also, P-value is given by the following formula;</u>
P-value = P(Z < -2.05) = 1 - P(Z 2.05)
= 1 - 0.97982 = <u>0.0202</u> or 2.02%
<em>Now at 5% significance level, the z table gives critical values between -1.96 and 1.96 for two-tailed test. Since our test statistics does not lies within the range of critical values of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.</em>
Therefore, we conclude that the proportion of dropouts has changed from the historical value of 0.081.