A Statistics professor has observed that for several years about 12% of the stud

Question

A Statistics professor has observed that for several years about 12% 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,194 students signed up for the Statistics course. They used the software suggested, and only 13 dropped out of the course.

1) Write the Hypothesis's: Ho and Ha

2) Compute the test statistic. Select the correct choice below, and, if necessary, fill in the answer box to complete your choice.

3) Calculate the P-value. Select the correct choice below, and, if necessary, fill in the answer box to complete your choice.

4) Should the professor spend the money for this software? Is the p value greater or less than a? Do you reject Ho?

5) Explain what your P-value means in this context. Select the correct choice below, and, if necessary, fill in the answer box to complete your choice.

- The chance of observing 13 or fewer dropouts in a class of 194 is ____ % if the dropout rate is really 12%

- The chance of observing 13 or more dropouts in a class of 194 is ____ % if the dropout rate is really 12%

-The P-value cannot be calculated. The conditions for a hypothesis test are not all met.

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.12
HA : p < 0.12

Hypothesis test results:

Hence,

1) Hypotheses:

Ho: p = 0.12

Ha: p < 0.12

2) Test statistic = -2.27

3) P - value = 0.0116

4) If level of significane is greater than 0.0116 then we reject the null hypothesis and conclude that there is enough evidence to support the claim that statistical software package reduced the dropout rate and hence, professor should spend money on the software.

5) Option B; The chance of observing 13 or more dropouts in a class of 194 is 1.16 % if the dropout rate is really 12%.

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