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Hypothesis Testing for Number of Seniors Planning to Attend College

Results from previous studies showed 79% 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.

1. State the null and alternative hypotheses.

A. H0:  = .79, H1:  > .79
B. H0: p = .79, H1: p ≠ .79
C. H0: p ≤ .79, H1: p > .79
D. H0: = .79, H1: > .79

Please note that the symbol in A is u, population mean. Also see attachment for clarification.

2. Compute the z or t value of the sample test statistic.

A. z = 0.69
B. t = 1.645
C. z = 1.96
D. z = 0.62

3. What is your conclusion?

A. Do not reject H0. There is not enough evidence to support the claim that the proportion of students planning to go to college is greater than .79.
B. Reject H0. There is enough evidence to support the claim that the proportion of students planning to go to college is now greater than .79.
C. Cannot determine
D. More seniors are going to college

4. What is the p-value associated with your test of hypothesis?

A. 0.7563
B. 0.6874
C. 0.4874
D. 0.2437

Please show steps.

Solution Preview

Before we get started with this particular question, I'd like to point you to a very useful website that discusses how to do these types of hypothesis testing problems in detail. http://www.acastat.com/Statbook/ztest1.htm

1. These choices all appear very peculiar. A is obviously wrong, because we are dealing with proportions here, so we should be looking ...

Solution Summary

Four questions on p-value, hypothesis rejection and hypothesis testing in general are answered. The null and alternative hypothesis are stated.

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