Significance Test for a Mean Section 9.2 Day 4 Significance Test for a Mean

Your grade in your statistics class is not all what you had hoped it would be. You took five exams, each worth 100 points. Your scores were 52, 63, 72, 41, and 73. Your teacher averages these scores, gets 60.2, and says you have earned a D.

You think what you have learned about a confidence interval for a mean can help you convince your teacher to give you a C, which is a mean score between 70 and 79.

You remember that your teacher told your class at the beginning of the year that the questions on the exams would be only a random sample of thousands of questions that he could ask. Write an explanation that supports your argument that you should receive a C rather than a D.

Page 578, E8 (modified) Your grade in your statistics class is not all that you had hoped it would be. You took five exams, each worth 100 points. Your scores were 52, 63, 72, 41, and 73. Your teacher averages these scores, gets 60.2, and says you have earned a D. You think what you have learned about a confidence interval for a mean can help you convince your teacher to give you a C, which is a mean score between 70 and 79. You remember that your teacher told your class at the beginning of the year that the questions on the exams would be only a random sample of the thousands of questions that he could ask. Write an explanation that supports your argument that you should receive a C rather than a D.

Conditions (1) Randomness: scores on the 5 exams can be considered random sample as the questions on the exams were a random sample that could be asked.

Conditions (1) Randomness: scores on the 5 exams can be considered random sample as the questions on the exams were a random sample that could be asked. (2) Normality: boxplot shows fairly symmetric pattern with no outlier so reasonable to assume sample came from normally distributed population

Conditions (3) Population size: population is thousands of questions so population is at least 10 times the sample size

95% CI: (43.234, 77.166)

95% CI: (43.234, 77.166) A population mean from 70 to 77.166 is reasonably likely to have produced results like these test scores.

95% CI: (43.234, 77.166) A population mean from 70 to 77.166 is reasonably likely to have produced results like these test scores. Therefore, the student could plausibly be a C student in stats.

Page 600, E31

Page 600, E31 A P-value measures D. The probability of seeing a value of t at least as extreme as the one observed, given that the null hypothesis is true/

Page 601, E35

E35 The two probabilities are the same: Both are equal to 0.05. P(Type I error) = α

Page 601, E36

Page 601, E36 Because α is equal to the probability of making a Type I error, a test with α = 0.05 has a larger chance of a Type I error than a test with α = 0.01.

Page 600, E32 Select each correct description of the power of a test.

Page 600, E32 Select each correct description of the power of a test. A. gives probability of rejecting null hypothesis C. increases by increasing sample size D. increases by increasing level of significance,α

Page 601, E37

Page 601, E37 a. a test with α = 0.10

Page 601, E37 a. a test with α = 0.10 b. a test with n = 45

Page 601, E37 a. a test with α = 0.10 b. a test with n = 45 c. a one-sided test (assuming the alternative hypothesis is in the correct direction)

Page 601, E39 Only part b.

Page 601, E39 b. Histogram B is the distribution of t-values because this distribution has a larger spread than Histogram A.

Questions? Quiz 9.1 - 9.2 both sides of a note card