Results from previous studies showed 76% of all high school seniors from a certain city plan to attend college after graduation.

Question

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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. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance.

Mathematics

1 answer:

babunello [11.8K] · Answer 1 · 2026-03-16T07:56:28+03:00

Answer:

Yes, this suggests that there has been an increase compared to earlier studies.

Step-by-step explanation:

The previous studies indicated that 76% of high school seniors from a particular city intended to pursue college after graduation.

A random sample consisting of 200 high school seniors from this city shows that 162 intend to attend college.

Let p denote the percentage of all high school seniors from this particular city who plan to enroll in college after graduating

Thus, Null Hypothesis: p $H_0$ 76% {indicating no increase from earlier studies} $\leq$

Alternate Hypothesis $H_a$ : p > 76% {indicating an increase over previous studies}

The test statistic used here is One-sample z proportion statistics;

T.S. =

~ N(0,1) $\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }$

where,

= sample proportion of high school seniors from this city who $\hat p$

plan to attend college =

= 0.81 $\frac{162}{200}$

n = sample of high school seniors = 200

Thus,

test statistics = $\frac{0.81-0.76}{{\sqrt{\frac{0.81(1-0.81)}{200} } } } }$

= 1.8025

At a 5% significance level, the z table indicates a critical value of 1.6449 for a right-tailed test. Since our test statistic exceeds this critical value, we have substantial evidence to reject the null hypothesis, as it resides in the rejection zone.

Therefore, we conclude that the percentage has indeed risen from earlier studies.