A Statistics professor has observed that for several years about 15% of the stud

Question

A Statistics professor has observed that for several years about 15% of the students who initially enroll in his Introductory Statistics course withdraw before the end of the semester. A salesman suggests that he try a statistics software package that gets students more involved with computers, predicting that it will cut the dropout rate. The professor can use the software free of charge for one semester as part of a trial package. Initially, 182 students signed up for the Statistics course. They used the software suggested, and only 12 dropped out of the course. Complete parts a and b below. a) Should the professor spend the money for this software? Support your recommendation with an appropriate test. Use ?=0.05 Assume 182 0.0659 Ha: p#0.15 HA p 0.15 Ho:p=0.0659 HA: p

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P > 0.15
Alternative hypothesis: P < 0.15

Note that these hypotheses constitute a one-tailed test.  

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.02647
z = (p - P) / S.D

z = - 3.18

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than -3.18.

Thus, the P-value = 0.006

Interpret results. Since the P-value (0.006) is less than the significance level (0.05), we cannot accept the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that dropout rate has decreased.

D) Yes, because the p-value is less than alpha. Reject H0 and conclude that there is strong evidence that dropout rate has fallen.

b) (A) The chance of observing 12 or fewer dropouts in a class of 182 is 6.59% if the dropout rate is really 15%.

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