It is found out that 13% of students enrolled in College Algebra at a large university fail the first time they take it. A psychology professor claims that this could be reduced with a program of counseling, and so on. A random sample of 850 students enrolled in College Algebra take this program and 99 fail anyway. Is this a significant improvement at the 0.05 level?
Hypothesized Population Proportion
Favorable Cases
Sample Size
Sample Proportion
Significance Level
The following null and alternative hypotheses for the population proportion needs to be tested:
This corresponds to a left-tailed test, for which a z-test for one population proportion will be used.
Based on the information provided, the significance level is and the critical value for a left-tailed test is
The rejection region for this left-tailed test is
The z-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population proportion is less than at the significance level.
Using the P-value approach:
The p-value is and since it is concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population proportion is less than at the significance level.
Therefore, there is not enough evidence to claim that this is a significant improvement at the 0.05 level.
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