Answer:
Yes, this indicate that the percentage has increased from that of previous studies.
Step-by-step explanation:
We are given that Results from previous studies showed 76% of all high school seniors from a certain city plan to attend college after graduation.
A random sample of 200 high school seniors from this city reveals that 162 plan to attend college.
<em>Let p = % of all high school seniors from a certain city who plan to attend college after graduation</em>
SO, <u>Null Hypothesis</u>, : p
76% {means that the percentage has not increased from that of previous studies}
<u>Alternate Hypothesis,</u> : p > 76% {means that the percentage has increased from that of previous studies}
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 seniors from this city who
plan to attend college = = 0.81
n = sample of high school seniors = 200
So, <u><em>test statistics</em></u> =
= 1.8025
<em>Now at 5% significance level, the z table gives critical value of 1.6449 for right-tailed test. Since our test statistics is more than the critical value 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 percentage has increased from that of previous studies.