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.
Construc...
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.
That is correct!
$$(67, 87)
Answer Explanation
Correct answers:
$\left(67,\ 87\right)$(67, 87)
A confidence interval is an interval of values, centered on a point estimate, of the form
(pointestimate−marginof error,pointestimate+marginof
error)
Using the given point estimate for the mean, x¯=77 and margin of error 10, the confidence interval is:
(77−10,77+10)(67,87)
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Question 2 A random sample of adults were asked whether they prefer reading an e-book over a printed book. The survey resulted in a sample proportion of p′=0.14, with a sampling standard deviation of σp′=0.02, who preferred reading an e-book.
Use the empirical rule to construct a 95% confidence interval for the true proportion of adults who prefer e-books.
That is correct!
$$(0.1, 0.18)
Answer Explanation
Correct answers:
$\left(0.10,\ 0.18\right)$(0.10, 0.18)
By the Empirical Rule, a 95% confidence interval corresponds to a z-score of z=2. Substituting the given values p′=0.14and σp′=0.02, a confidence interval is
(p′−z⋅σp′,p′+z⋅σp′)(0.14−2⋅0.02,0.14+2⋅0.02)
(0.14−0.04,0.14+0.04)(0.10,0.18)
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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.
Answer Explanation
Correct answer:
We estimate with 95% confidence that the true population mean is between 237 and 293 pages.
Once a confidence interval is calculated, the interpretation should clearly state the confidence level (CL), explain what population parameter is being estimated, and state the confidence interval.
We estimate with 95% confidence that the true population mean is between 237 and 293 pages.
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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?
z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576
Use the table above for the z-score, and be sure to round up to the nearest integer.
That is correct!
$$14 dog heights
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