MATHEMATICS

 

D. None of the lines is the line of best

 

 

23.              A researcher wishes to estimate the mean amount of money spent per month on food by households in a certain neighborhood. She desires a margin of error of $30. Past studies suggest that a population standard deviation of $248 is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.

A. 274        B. 284      C. 264        D. 272

 

Again, assuming a 95% confidence interval, with z = 2.00 instead of 1.96:

 

n = (z * s / E)2 = (2 * 248 / 30)2 = 273.35 à 274

 

24.           Suggest the cause of the correlation among the data.

 

The graph shows strength of coffee (y) and number of scoops used to make 10 cups of coffee (x). Identify the probable cause of the correlation.

 

 

A. The variation in the x variable is a direct cause of the variation in the y variable.
B. There is no correlation between the variables.
C. The correlation is due to a common underlying cause.
D. The correlation between the variables is coincidental

 

25.  Suggest the cause of the correlation among the data.

 

The graph shows strength of coffee (y) and number of scoops used to make 10 cups of coffee (x). Identify the probable cause of the correlation.

 

A.The variation in the x variable is a direct cause of the variation in
the y variable.
B. There is no correlation between the variables.
C. The correlation is due to a common underlying cause.
D. The correlation between the variables is coincidental.

26.A population proportion is to be estimated. Estimate the minimum sample size needed to achieve a margin of error E = 0.01with a 95% degree of confidence.

A. 7,000           B. 8,000              C. 9,000       D. 10,000

 

n = p(1-p)(z/E)2 = (0.5)(0.5)(2/0.01)2 = 10,000

 

27. Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram.

 

 

A. -0.9
B. 0.1
C. 0.5
D. 0.9

 

The slope of the regression line is negative, so the coefficient of correlation must

also be negative.

 

28. A sample of nine students is selected from among the students taking a particular exam. The nine students were asked how much time they had spent studying for the exam and the responses (in hours) were as follows:18, 7, 10, 13, 12, 16, 5, 20, 21

 

Estimate the mean study time of all students taking the exam. Round your answer to the nearest tenth of an hour if necessary.     A. 13 hours     B. 12.2 hours         C. 13.6 hours

D. It is not possible to estimate the population mean from this sample data

 

Mean = (18 + 7 + 10 + 13 + 12 + 16 + 5 + 20 + 21) / 9 = 13.6

29. The scatter plot and best-fit line show the relation among the data for the price of a stock (y) and employment (x) in arbitrary units. The correlation coefficient is 0.8. Predict the stock price for an employment value of 6.

 

 

A. 8.8
B. 6.2
C. 8.2
D. None of the values are correct

 

Draw a vertical line through “6” on the horizontal axis, and extend the line vertically until it intersects the line on the graph. Then draw a horizontal line through the point of intersection and extend that line to the left until it intersects the vertical axis. Read the value from the vertical axis, which is about 6.2.

 

 

 

 

 

 

30.The graph shows a measure of fitness (y) and miles walked weekly. Identify the probable cause of the correlation.

https://study.ashworthcollege.edu/access/content/group/8ef8b2f7-197d-41de-a4c4-db81a717c013/v9/Images/Lesson%206%20Exam/MA260%20Lesson%206%20exam%20question%204.JPG

 

A. The correlation is coincidental.
B. There is a common underlying cause of the correlation.
C. There is no correlation between the variables.
D. Walking is a direct cause of the fitness.

 

 

31. Eleven female college students are selected at random and asked their heights. The heights (in inches) are as follows:67, 59, 64, 69, 65, 65, 66, 64, 62, 64, 62Estimate the mean height of all female students at this college. Round your answer to the nearest tenth of an inch if necessary.

 

A. It is not possible to estimate the population mean from this sample data
B. 64.3 inches
C. 64.9 inches
D. 63.7 inches

 

Mean = (67 + 59 + 64 + 69 + 65 + 65 + 66 + 64 + 62 + 64 + 62) / 11 = 64.3

32. Select the best fit line on the scatter diagram below.

 

 

 

A. A

B. B
C. C
D. All of the lines are equally good

 

33. In a poll of 400 voters in a certain state, 61% said that they opposed a voter ID bill that might hinder some legitimate voters from voting. The margin of error in the poll was reported as 4 percentage points (with a 95% degree of confidence). Which statement is correct?

A. The reported margin of error is consistent with the sample size.

B. There is not enough information to determine whether the margin of error is consistent with the sample size.

C. The sample size is too small to achieve the stated margin of error.

D. For the given sample size, the margin of error should be smaller than stated

     Required sample size = (phat)(1 – phat)(z/E)2 = (0.61)(1 – 0.61)(2/0.04)2 = 594.75

34.The scatter plot and best-fit line show the relation among the number of cars waiting by a school (y) and the amount of time after the end of classes (x) in arbitrary units. The correlation coefficient is -0.55. Determine the amount of variation in the number of cars not explained by the variation time after schhttps://study.ashworthcollege.edu/access/content/group/8ef8b2f7-197d-41de-a4c4-db81a717c013/v9/Images/Lesson%206%20Exam/MA260%20Lesson%206%20exam%20question%206.JPG

 

A. 55%
B. 70%
C. 30%
D. 45%

 

Coefficient of non-determination = 1 – r2 = 1 – (-0.55)2 = 0.6975 → 70%

 

35. Which graph has two groups of data, correlations within each group, but no correlation among all the data?

 

 

A.

 

 

B.

 

 

C.

 

 

D

https://study.ashworthcollege.edu/access/content/group/8ef8b2f7-197d-41de-a4c4-db81a717c013/v9/Images/Lesson%206%20Exam/MA260%20Lesson%206%20exam%20question%203%20_D_.JPG

36. The scatter plot and best-fit line show the relation among the number of cars waiting by a school (y) and the amount of time after the end of classes (x) in arbitrary units. The correlation coefficient is -0.55. Use the line of best fit to predict the number of cars at time 4 after the end of classes.

https://study.ashworthcollege.edu/access/content/group/8ef8b2f7-197d-41de-a4c4-db81a717c013/v9/Images/Lesson%206%20Exam/MA260%20Lesson%206%20exam%20question%2013.JPG

 

A. 7.0
B. 6.0
C. 8.0
D. 3.5

 

Draw a vertical line through the value 4 on the horizontal axis and extend the line vertically until it intersects the line shown on the graph. Then draw a horizontal line through the point of intersection and extend it to the left until it intersects the vertical axis. Read the value where the horizontal line crosses the vertical axis. The value is approximately 7.

 

37. A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 560 college students showed that 27% of them had, or intended to, cheat on examinations. Find the 95% confidence interval.

A. 0.2323 to 0.3075

B. 0.2325 to 0.3075

C. 0.2325 to 0.3185

D. 0.2323 to 0.3185

 

Lower limit = phat – z*sqrt(phat*(1 – phat)/n)

Lower limit = 0.27 – 2*sqrt(0.27*0.73/560)

Lower limit = 0.2325

 

Upper limit = phat+ z*sqrt(phat*(1 – phat)/n)

Upper limit = 0.27 + 2*sqrt(0.27*0.73/560)

Upper limit = 0.3075

 

 

 

 

 

 

 

38. Among a random sample of 150 employees of a particular company, the mean commute distance is 29.6 miles. This mean lies 1.2 standard deviations above the mean of the sampling distribution. If a second sample of 150 employees is selected, what is the probability that for the second sample, the mean commute distance will be less than 29.6 miles?

A. 0.8849           B. 0.5          C. 0.1131        D. 0.1151

 

P(second sample mean ≤ 29.6) = P(z ≤ 1.2) = 0.8849

 

39. The scatter plot and best-fit line show the relation between the price per item (y) and the availability of that item (x) in arbitrary units. The correlation coefficient is -0.95. Determine the amount of variation in pricing explained by the variation in availability.

https://study.ashworthcollege.edu/access/content/group/8ef8b2f7-197d-41de-a4c4-db81a717c013/v9/Images/Lesson%206%20Exam/MA260%20Lesson%206%20exam%20question%2012.JPG

 

A. 5%
B. 10%
C. 95%
D. 90%

 

Coefficient of determination = r2 = (-0.95)2 = 0.9025 ≈ 90%

 

40. Of the 6796 students in one school district, 1537 cannot read up to grade level. Among a sample of 812 of the students from this school district, 211 cannot read up to grade level. Find the sample proportion of students who cannot read up to grade level       A. 0.14        B. 0.26      C. 211      D. 0.23

 

phat = x/n = 211 / 812 = 0.26

 

 

 

 

 

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