Question

This quiz covers the first half of Section 7.1 (constructing confidence intervals using t statistics) and is due at 9:00 PM on Thursday, April 2.

You will have two attempts at this quiz. I suggest you do all of them first on paper. After the first attempt, you should write down which ones you answered correctly and which one incorrectly, as well as any hints that were given. Then re-solve the problems and take the quiz a second time. Note that the responses will appear in a different order the second time you take the quiz. Correct answers will appear on Canvas, twenty four hours after the quiz is due.

By submitting this quiz you affirm you did not receive any help from anyone in completing the quiz, except for clarifications provided by the instructor.  Using the videos, textbook and handbook is acceptable.

Question 11 pts

William Gosset worked in quality control for a major beverage company. He developed the t-distribution to:

Group of answer choices

monitor the sugar content of Pretty Things craft beer.

improve the consistency of Guinness ale.

determine if drinking Gallo's Zinfandel red wine decreased heart attack risk,

compare the richness of Nescafe regular and decaf coffees.

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Question 21 pts

A t distribution is used in constructing confidence intervals for all the following reasons EXCEPT:

Group of answer choices

To account for the extra uncertainty when the population standard deviation (sigma) is unknown.

When the sample size is too large to use z statistics.

When we use the sample standard deviation (s) in constructing the margin of error.

When we do not have any historical data that can help us make our estimate.

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Question 31 pts

When computing the margin of error (MOE) using a t-distribution, the following are all true EXCEPT:

Group of answer choices

The MOE increases when t* is used in place of z*.

The MOE increases when the degrees of freedom (df) increases.

The MOE increases when the standard error of the mean increases.

The MOE increases when a higher confidence level is used.

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Question 41 pts

Questions 4 through 7 are the steps required to solve Exercise #7.30(a) on IPS p. 428. This study investigates the hours per month spent on the Internet by U.S. residents, age 18 to 24. The sample results are: n= 75, x-bar=28.5, and s=23.1 . We are to construct a 95% confidence interval based on this information.

What is critical value of t (that is, t*) for this confidence interval?

Group of answer choices

1.960

1.990

2.000

2.009

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Question 51 pts

Continuing Question 4, the standard error of the mean (SEM) is:

Group of answer choices

.3080

23.10

2.685

2.667

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Question 61 pts

Rounded to one decimal place, as x-bar was, the margin of error (MOE) for your confidence interval will be:

Group of answer choices

4.7

5.9

5.6

5.3

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Question 71 pts

Which of the following conclusions is CORRECT?

Group of answer choices

We are 95% sure the mean hours spent per month on the Internet by college students is between 23.2 and 33.8.

We are 95% sure the mean hours spent per month on the Internet by U.S. residents, age 18 to 24, is between 23.5 and 34.1.

We are 95% sure the mean hours spent per month on the Internet by U.S. residents, age 18 to 24, is between 23.2 and 33.8.

We are 95% sure the mean hours spent per week on the Internet by U.S. residents, age 18 to 24, is between 23.5 and 34.1.

Answer 1

Question 11

Answer: determine if drinking Gallo's Zinfandel red wine decreased heart attack risk

Question 21

Answer:When the sample size is too large to use z statistics.

reason : if the sample size is large z score test are more appropriate and reliable

Question 31

Answer:The MOE increases when the degrees of freedom (df) increases.

Reason the MOE decreases when degree of freedom increases because the cricitcal value decreases as fegree of freedom increases and MOE is directly proprtional to critical value.

Question 41

Answer: 1.99

Question 51

Answer :2.667

Reason: sample sigma / square root of n

Standard error of mean=

Question 61

Answer : 5.3

Reason:1.99*2.667

SEM * CV ( t distribution)= MARGIN OF ERROR

Question 71

Answer : We are 95% sure the mean hours spent per month on the Internet by U.S. residents, age 18 to 24, is between 23.2 and 33.8.

Reason : xbar = 28.5 ,moe= 5.3

confidence interval = (xbar - margin of error , xbar - margin of error)