compared. The means and standard deviations for groups A and B are determined as well as the mean
and standard deviation for the difference between each twin’s score. Is this study a one-sample or
two-sample situation, and how many degrees of freedom are involved in determining the t -value?
Which of the following statements is (are) correct? Explain.
I. A confidence interval can be used instead of a test statistic in any hypothesis test involving
means or proportions.
II. A confidence interval can be used instead of a test statistic in a two-sided hypothesis test
involving means or proportions.
III. The standard error for constructing a confidence interval for a population proportion and the
standard error for a significance test for a population proportion are the same.
IV. The standard error for constructing a confidence interval for a population mean and the standard
error for a significance test for a population mean are the same.
The average math SAT score at Hormone High School over the years is 520. The mathematics faculty
believes that this year’s class of seniors is the best the school has ever had in mathematics. One
hundred seventy-five seniors take the exam and achieve an average score of 531 with a sample
standard deviation of 96. Does this performance provide good statistical evidence that this year’s
class is, in fact, superior?
- An avid reader, Booker Worm, claims that he reads books that average more than 375 pages in
length. A random sample of 13 books on his shelf had the following number of pages: 595, 353, 434,
382, 420, 225, 408, 422, 315, 502, 503, 384, 420. Do the data support Booker’s claim? Test at the
0.05 level of significance. - The statistics teacher, Dr. Tukey, gave a 50-point quiz to his class of 10 students and they didn’t do
very well, at least by Dr. Tukey’s standards (which are quite high). Rather than continuing to the next
chapter, he spent some time reviewing the material and then gave another quiz. The quizzes were
comparable in length and difficulty. The results of the two quizzes were as follows.
Do the data indicate that the review was successful, at the .05 level, at improving the performance of
the students on this material? Give statistical evidence for your conclusion.
The new reality TV show, “I Want to Marry a Statistician,” has been showing on Monday evenings,
and ratings show that it has been watched by 55% of the viewing audience each week. The producers
are moving the show to Wednesday night but are concerned that such a move might reduce the
percentage of the viewing public watching the show. After the show has been moved, a random
sample of 500 people who are watching television on Wednesday night are surveyed and asked what
show they are watching. Two hundred fifty-five respond that they are watching “I Want to Marry a
Statistician.” Does this finding provide evidence at the 0.01 level of significance that the percentage
of the viewing public watching “I Want to Marry a Statistician” has declined?
- Harvey is running for student body president. A survey is conducted by the AP Statistics class in an
attempt to predict the outcome of the election. They randomly sample 30 students, 16 of whom say
they plan to vote for Harvey. Harvey figures (correctly) that 53.3% of students in the sample intend to