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, 177 students signed up for the Statistics course. They used the software suggested, and only 15 dropped out of the course. Complete parts a and b below. 0.05. Assume 177 10% of all students a) Should the professor spend the money for this software? Support your recommendation with an appropriate test. Use? who have taken the class with the professor Determine the hypotheses for this test. Choose the correct answer below O A. Ho: p 0.12 O B. Ho:p#0.0847 HA: p #0.0847 HA p0.12 Ha: p > 0.12 HA p0.0847 Ho:p#0.12 Ha: p#0.12 ? E. Ho : p :0.0847 F. Compute the test statistic. Select the correct choice below, and, if necessary, fill in the answer box to complete your choice 0 A. | (Round to two decimal places as needed.) B. The test statistic cannot be calculated. The conditions for a hypothesis test are not all met. Calculate the P-value. Select the correct choice below, and, if necessary, fill in the answer box to complete your choice O A. (Round to four decimal places as needed.) O B. The P-value cannot be calculated. The conditions for a hypothesis test are not all met. Should the professor spend the money for this software? ? A. No, because the P-value is greater than ?. Do not reject Ho and conclude that there is no strong evidence that the dropout rate has fallen. ? B. Yes, because the P-value is less than ?, Reject Ho and conclude that there is strong evidence that the dropout rate has fallen. ° C. Yes, because the P-value is greater than ?, Reject Ho and conclude that there is strong evidence that the dropout rate has fallen. d D. No, because the P-value is less than ?. Do not reject Ho and conclude that there is no strong evidence that the dropout rate has fallen. O E. No conclusion can be made. The conditions for a hypothesis test are not all met. b) 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. A. The chance of observing 15 or fewer dropouts in a class of 177 is (Round to two decimal places as needed.) The chance of observing 15 or more dropouts in a class of 177 is Round to two decimal places as needed.) The P-value cannot be calculated. The conditions for a hypothesis test are not all met. % if the dropout rate is really 12%. B. % if the dropout rate is really 12%. ° C.

Explanation / Answer

H0: p = 0.12

Ha: p < 0.12

pcap = 15/177 = 0.0847

Test statistics,

z = (0.0847 - 0.12)/sqrt(0.12*0.88/177)

z = -1.4452

p-value = 0.0742

No, because p-value is greater than alpha. Do not reject H0. Option (A)

b)

The chance of observing 15 or fewer dropouts in a class of 177 is 7.42% if the dropout rate is really 12%

Confidence interval

n = 32

mean = 710

z-value of 95% CI = 1.9600

std. dev. = 65

SE = std.dev./sqrt(n)

= 65/sqrt(32)

= 11.49

ME = z*SE

= 1.96*11.49

= 22.5209

Lower Limit = Mean - ME = 687.47906

Upper Limit = Mean + ME = 732.52094

95% CI (687 , 733)

b)

Option B

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