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# Regression analysis and Confidence interval

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Question 1
A random sample of 85 students in Chicago's city high schools take a course designed to improve SAT scores. Based on this sample, a 90% confidence interval for the mean improvement &#956; in SAT score for all Chicago city high school students taking this course is found to be (72.3, 91.4). Which of the following statements is the correct interpretation of this interval?

a)Ninety percent of the students in the sample improved their scores by between 72.3 and 91.4 points.

b)Ninety percent of the students in the population who take the course should improve their scores by between 72.3 and 91.4 points.

c)If we constructed this interval multiple times, 90% of the intervals would include the true mean.

d)None of the above is correct.

Question 2
A random sample of size n is collected from a normal population with standard deviation &#963;. Using these data, a confidence interval is computed for the mean of the population. Which of the following actions would produce a new confidence interval with a smaller width (smaller margin of error), assuming that the same data were used?

a)increasing the value of &#963;

b)using a lower confidence level

c)using a smaller sample size n

d)all of the above.

Question 3
The heights (in inches) of adult males in the United States are believed to be normally distributed with mean &#956;. The average height of a random sample of 25 American adult males is found to be = 69.72 inches, with a sample standard deviation of s = 4.15 inches. A 90% confidence interval for &#956; is

a)69.72 ± 1.42.

b)69.72 ± 1.09.

c)69.72 ± 1.37.

d)69.72 + .90

Question 4
A radio talk show host is interested in the proportion p of adults in his listening area who think that the drinking age should be lowered to 18. To find this proportion, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to 18 in light of the fact that 18-year-olds are eligible for military service?" He asks listeners to phone in and vote "yes" or "no" depending upon their opinions. Of 200 people who phone in, 140 answer "yes." The standard error of the sample proportion of "yes" votes among those who phone in is

a)0.84

b)0.032.

c).002

d)0.00105.

Question 5
Foresters use linear regression to predict the volume of timber in a tree using easily measured quantities such as diameter. Let y be the volume of timber in cubic feet produced by a tree and let x be the tree's diameter in feet (measured at a height of 3 feet above the ground). One set of paired data gives the prediction equation

= -30 + 60x

The predicted volume of timber for a tree of diameter 18 inches is

a)1050 cubic feet.

b)1010 cubic feet.

c)90 cubic feet.

d)60 cubic feet.

QUESTION 6: ...SEE ATTACHED WORD FILE...

Question 7
A study showed that students who spend more time studying for statistics tests tend to achieve better scores on their tests. In fact, the number of hours studied turned out to explain 81% of the observed variation in test scores among the students who participated in the study. What is the value of the correlation between number of hours studied and test score?

a)r = 0.81

b)r = -0.656

c)r = 0.656

d)r = 0.9.

Question 8
There is a strongly linear association between the weight of a football player and the time in seconds it takes for that player to run a 100-yard dash. Knowing this, a reasonable value for the correlation r between weight and 100-yard dash time would be

a)r = 0.8.

b)r = 0.

c)r = -0.8.

d)r =-1.2

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#### Solution Summary

The solution provides step by step method for the calculation of confidence interval and regression model for a number of questions. Formula for the calculation and Interpretations of the results are also included.

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