Download MATH225 Week 6 Quiz: Confidence Intervals and Sampling Distributions and more Exams Nursing in PDF only on Docsity!
MATH225 Week 6 Quiz
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.
That is correct!
Answer: (67, 87)
Question 2
A random sample of adults were asked whether they prefer reading an e-book 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. That is correct!
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?
That is correct! 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. That is correct! 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.
Use the table of values above. That is correct!
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 516 536 462 461 519 496 517 488 521 HelpCopy to ClipboardDownload CSV That is correct! Answer: (509.30, 519.18)
A sample of 27 employees for the Department of Health and Human Services has the following salaries, in
thousands of dollars. Assuming normality, use Excel to find the 98% confidence interval for the true mean
salary, in thousands of dollars. Round your answers to two decimal places and use increasing order. Salary 71 70 69 65 72 69 72 72 71 HelpCopy to ClipboardDownload CSV That is correct!
Answer: (69.14, 71.38)
Question 10
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 1 inch of the true population mean, what is the minimum
sample size that can be taken?
z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.
Use the table above for the z-score, and be sure to round up to the nearest integer.
That is correct!
Answer: 53 dog heights
Question 11
A random sample of house sizes in major city has a sample mean of x¯=1204.9 sq ft and sample standard
deviation of s=124.6 sq ft. Use the Empirical Rule to determine the approximate percentage of house
sizes that lie between 955.7and 1454.1 sq ft.
Round your answer to the nearest whole number (percent).
That is correct!
Answer: 95%
Question 12
The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis.
Determine which normal distribution has the smallest standard deviation. That is correct! A B C
Question 13
The resistance of a strain gauge is normally distributed with a mean of 100 ohms and a standard deviation
of 0.3 ohms. To meet the specification, the resistance must be within the range 100±0.7 ohms. What
proportion of gauges is acceptable? Round your answer to four decimal places. That is correct!
Answer: 0.
Question 14
Question 16
An elementary school has a population of 635 students, 600 of whom have received the chicken
pox vaccine. The school nurse wants to make sure that the school meets all state requirements for vaccinations at public schools. Find the population proportion, as well as the mean and standard deviation of the sampling
distribution for samples of size n=120.
Round all answers to 3 decimal places. That is correct!
p = 0.
μp ̂ = 0.
σp ̂ = 0.
Question 17
The lengths of text messages are normally distributed with an unknown population mean. A random
sample of text messages is taken and results in a 95% confidence interval of (23,47) characters.
What is the correct interpretation of the 95% confidence interval?
That is correct! We estimate that 95% of text messages have lengths between 23 and 47 characters. We estimate with 95% confidence that the true population mean is between 23 and 47 characters. We estimate with 95% confidence that the sample mean is between 23 and 47 characters.
Question 18
Given the plot of normal distributions A and B below, which of the following statements is true? Select all
correct answers.
A normal bell curve labeled Upper A and a normal elongated curve labeled Upper B are centered at the same point. Normal curve Upper B is narrower and above normal curve Upper A. That is correct!
A has the larger mean.
B has the larger mean.
The means of A and B are equal.
A has the larger standard deviation.
B has the larger standard deviation.
The standard deviations of A and B are equal.
Question 19
HelpCopy to ClipboardDownload CSV That is correct! Answer: (894.43, 940.21)
Question 22
Hugo averages 40 words per minute on a typing test with a standard deviation of 15 words per minute.
Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per
minute on a typing test. Then, X∼N(40,15).
Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is
________. This z-score tells you that x=56 is ________ standard deviations to the ________ (right/left) of
the mean, ________. Correctly fill in the blanks in the statement above. That is correct! Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −0.889. This z-score tells you that x=56 is 0.889 standard deviations to the left of the mean, 40. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −1.067. This z-score tells you that x=56 is 1.067 standard deviations to the left of the mean, 40. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is 1.067. This z-score tells you that x=56 is 1.067 standard deviations to the right of the mean, 40. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is 0.889. This z-score tells you that x=56 is 0.889 standard deviations to the right of the mean, 40.
Question 23
Hugo averages 62 words per minute on a typing test with a standard deviation of 8 words per minute.
Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per
minute on a typing test. Then, X∼N(62,8).
Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is
________. This z-score tells you that x=56 is ________ standard deviations to the ________ (right/left) of
the mean, ________. Correctly fill in the blanks in the statement above. That is correct! Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is 0.75. This z-score tells you that x=56 is 0.75 standard deviations to the right of the mean, 62. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −0.75. This z-score tells you that x=56 is 0.75 standard deviations to the left of the mean, 62. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is 0.545. This z-score tells you that x=56 is 0.545 standard deviations to the right of the mean, 62. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −0.545. This z-score tells you that x=56 is 0.545 standard deviations to the left of the mean, 62.
Question 24
Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution.
What is the probability that a randomly selected book has fewer than 168 pages if the mean is 190 pages
and the standard deviation is 22 pages? Use the empirical rule.Enter your answer as a percent rounded to
two decimal places if necessary. That is correct!
Answer: 15.87%
Question 25
Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution.
What is the probability that a randomly selected book has fewer than 140 pages if the mean is 190 pages
and the standard deviation is 25 pages? Use the empirical rule.Enter your answer as a percent rounded to
two decimal places if necessary. That is correct!
Correct answers: 2.5%
