a statistics professor has observed that for several years students score an average of 105 points out of 150 on the semester exam. A salesman suggests that he try a statistics software package that gets students more involved with computers, predicting that it will increase students\' scores. The software is expensive, and the salesman offers to let the professor use it for a semester to see if the scores on the final exam increase significantly. The professor will have to pay for the software only if he chooses to continue using it.
A) is this a one tailed or two tailed test? Explain.
B) write the null and alternative hypotheses:
C) in this context, explain what would happen if the professor makes a Type 1 error
D) in this context, explain what would happen if the professor makes a Type 2 error:
a statistics professor has observed that for several years students score an average of 105 points out of 150 on the semester exam. A salesman suggests that he try a statistics software package that gets students more involved with computers, predicting that it will increase students\' scores. The software is expensive, and the salesman offers to let the professor use it for a semester to see if the scores on the final exam increase significantly. The professor will have to pay for the software only if he chooses to continue using it.
A) is this a one tailed or two tailed test? Explain.
B) write the null and alternative hypotheses:
C) in this context, explain what would happen if the professor makes a Type 1 error
D) in this context, explain what would happen if the professor makes a Type 2 error:
a statistics professor has observed that for several years students score an average of 105 points out of 150 on the semester exam. A salesman suggests that he try a statistics software package that gets students more involved with computers, predicting that it will increase students\' scores. The software is expensive, and the salesman offers to let the professor use it for a semester to see if the scores on the final exam increase significantly. The professor will have to pay for the software only if he chooses to continue using it.
A) is this a one tailed or two tailed test? Explain.
B) write the null and alternative hypotheses:
C) in this context, explain what would happen if the professor makes a Type 1 error
D) in this context, explain what would happen if the professor makes a Type 2 error:
A. This is a one-tailed test, as we are concerned with only an \'increase\' in the avergae marks and not in the decrease. So any significant deviation on the upside is our concern.
B. Null hypothesis: Average score after using software package = 105
Alternate hypothesis: Average score after using software package > 105
C. Type 1 error occurs when the Null is true, but rejected. So when the software package is actually not helpful and when the professor rejects the null, accepting the fact that the software package is helpful, then the professsor makes a Type 1 error.
D. Type 1 error occurs when the Null is false, but failed to reject. So when the software package is actually helpful and when the professor fails to reject the null, accepting the fact that the software package is not helpful, then the professsor makes a Type 2 error.
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