MATH 225N WEEK 6 QUIZ STATISTICS – QUESTION

AND ANSWERS

Question 1

A statistics professor recently graded final exams for students in her introductory

statistics course. In a review of her grading, she found the mean score out

of 100 points was a x¯=77, with a margin of error of 10.

Construct a confidence interval for the mean score (out of 100 points) on the

final exam.

Answer: (67, 87)

Question 2

A random sample of adults were asked whether they prefer reading an ebook over a printed book. The survey resulted in a sample proportion of p

′=0.14, with a sampling standard deviation of σp′=0.02, who preferred

reading an e-book.

Use the empirical rule to construct a 95% confidence interval for the true

proportion of adults who prefer e-books.

Answer: ( 0.10, 0.18)

Question 3

The pages per book in a library are normally distributed with an unknown

population mean. A random sample of books is taken and results in

a 95% confidence interval of (237,293) pages.

What is the correct interpretation of the 95% confidence interval?

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We estimate with 95% confidence that the sample mean is

between 237 and 293 pages.

We estimate that 95% of the time a book is selected, there will be

between 237 and 293 pages.

We estimate with 95% confidence that the true population mean is

between 237 and 293 pages.

Question 4

The population standard deviation for the heights of dogs, in inches, in a city

is 3.7 inches. If we want to be 95% confident that the sample mean is

within 2 inches of the true population mean, what is the minimum sample size

that can be taken? Round up to the nearest integer.

Answer: 14 dog heights

Question 5

Clarence wants to estimate the percentage of students who live more than three

miles from the school. He wants to create a 98% confidence interval which has

an error bound of at most 4%. How many students should be polled to create

the confidence interval?

z0.10 z0.05 z0.025 z0.01 z0.005

1.28

2

1.64

5

1.96

0

2.32

6

2.57

6

Use the table of values above.

Answer: 846 Students

Question 6

The average score of a random sample of 87 senior business majors at a

university who took a certain standardized test follows a normal distribution with

a standard deviation of 28. Use Excel to determine a 90% confidence interval

for the mean of the population. Round your answers to two decimal places and

use ascending order..

Score

516

536

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