Math 227 - Statistics » Spring 2023 » 19KC Scatterplots, Correlation, and Regression

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Question #1
Joe wishes to study the relationship between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR). The unemployment rate is the natural response variable. FRBIP, x 113 123 127 138 130 146 151 UR, y 3.1 1.9 1.7 1.6 3.2 2.7 2.6 Use the critical value method and a 5% significance level to test the claim of linear correlation. What population parameter is being tested?
A.   Mean
B.   Goodness-of-Fit or Independence or Homogeneity
C.   Linear Correlation Coefficient
D.   Proportion
E.   Standard Deviation or Variance
Question #2
Joe wishes to study the relationship between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR). The unemployment rate is the natural response variable. FRBIP, x 113 123 127 138 130 146 151 UR, y 3.1 1.9 1.7 1.6 3.2 2.7 2.6 Use the critical value method and a 5% significance level to test the claim of linear correlation. How many populations are being tested?
A.   More than two
B.   One
C.   Two
Question #3
Joe wishes to study the relationship between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR). The unemployment rate is the natural response variable. FRBIP, x 113 123 127 138 130 146 151 UR, y 3.1 1.9 1.7 1.6 3.2 2.7 2.6 Use the critical value method and a 5% significance level to test the claim of linear correlation. Calculate the sample linear correlation coefficient (round to the nearest ten-thousandth).
A.   -0.0999
B.   -0.0899
C.   -0.0599
D.   -0.0699
Question #4
Joe wishes to study the relationship between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR). The unemployment rate is the natural response variable. FRBIP, x 113 123 127 138 130 146 151 UR, y 3.1 1.9 1.7 1.6 3.2 2.7 2.6 Use the critical value method and a 5% significance level to test the claim of linear correlation. What is the claim? (At this point, you should have already selected the formula that will be used to calculate the test statistic and written it in the test statistic box.)
A.   ρ ≤ 0
B.   ρ ≠ 0
C.   ρ ≥ 0
D.   ρ > 0
E.   ρ < 0
F.   ρ = 0
Question #5
Joe wishes to study the relationship between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR). The unemployment rate is the natural response variable. FRBIP, x 113 123 127 138 130 146 151 UR, y 3.1 1.9 1.7 1.6 3.2 2.7 2.6 Use the critical value method and a 5% significance level to test the claim of linear correlation. The claim is the _________ hypothesis.
A.   null
B.   alternative
Question #6
Joe wishes to study the relationship between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR). The unemployment rate is the natural response variable. FRBIP, x 113 123 127 138 130 146 151 UR, y 3.1 1.9 1.7 1.6 3.2 2.7 2.6 Use the critical value method and a 5% significance level to test the claim of linear correlation. What is the alternative hypothesis?
A.   ρ ≤ 0
B.   ρ < 0
C.   ρ ≠ 0
D.   ρ > 0
E.   ρ ≥ 0
F.   ρ = 0
Question #7
Joe wishes to study the relationship between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR). The unemployment rate is the natural response variable. FRBIP, x 113 123 127 138 130 146 151 UR, y 3.1 1.9 1.7 1.6 3.2 2.7 2.6 Use the critical value method and a 5% significance level to test the claim of linear correlation. The critical region is best described as ____________.
A.   right-tailed
B.   two-tailed
C.   left-tailed
Question #8
Joe wishes to study the relationship between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR). The unemployment rate is the natural response variable. FRBIP, x 113 123 127 138 130 146 151 UR, y 3.1 1.9 1.7 1.6 3.2 2.7 2.6 Use the critical value method and a 5% significance level to test the claim of linear correlation. What is the significance level (expressed as a decimal)?
A.   0.07
B.   0.03
C.   0.01
D.   0.05
Question #9
Joe wishes to study the relationship between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR). The unemployment rate is the natural response variable. FRBIP, x 113 123 127 138 130 146 151 UR, y 3.1 1.9 1.7 1.6 3.2 2.7 2.6 Use the critical value method and a 5% significance level to test the claim of linear correlation. What is the largest critical value (rounded to the nearest thousandth)?
A.   2.291
B.   2.571
C.   2.331
D.   2.591
Question #10
Joe wishes to study the relationship between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR). The unemployment rate is the natural response variable. FRBIP, x 113 123 127 138 130 146 151 UR, y 3.1 1.9 1.7 1.6 3.2 2.7 2.6 Use the critical value method and a 5% significance level to test the claim of linear correlation. What is the test statistic (rounded to the nearest ten-thousandth)?
A.   -0.1357
B.   -0.1677
C.   -0.1567
D.   -0.2167
Question #11
Joe wishes to study the relationship between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR). The unemployment rate is the natural response variable. FRBIP, x 113 123 127 138 130 146 151 UR, y 3.1 1.9 1.7 1.6 3.2 2.7 2.6 Use the critical value method and a 5% significance level to test the claim of linear correlation. What is the statistical conclusion?
A.   Fail to reject H0.
B.   Reject H0.
Question #12
Joe wishes to study the relationship between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR). The unemployment rate is the natural response variable. FRBIP, x 113 123 127 138 130 146 151 UR, y 3.1 1.9 1.7 1.6 3.2 2.7 2.6 Use the critical value method and a 5% significance level to test the claim of linear correlation. What is the wordy conclusion?
A.   There is not sufficient evidence to warrant rejection of the claim of linear correlation between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR).
B.   There is sufficient evidence to support the claim of linear correlation between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR).
C.   There is sufficient evidence to warrant rejection of the claim of linear correlation between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR).
D.   There is not sufficient evidence to support the claim of linear correlation between the Federal Reserve Board index of industrial production (FRBIP) and the unemployment rate (UR).
Question #13
Jane wishes to study the relationship between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE). The height is the natural response variable. AGE, x 18 19 21 22 24 25 27 28 H, y 76.1 77 78.2 78.8 79.9 81.1 81.8 82.8 Use the p-value method and a 1% significance level to test the claim of linear correlation. What population parameter is being tested?
A.   Goodness-of-Fit or Independence or Homogeneity
B.   Linear Correlation Coefficient
C.   Standard Deviation or Variance
D.   Proportion
E.   Mean
Question #14
Jane wishes to study the relationship between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE). The height is the natural response variable. AGE, x 18 19 21 22 24 25 27 28 H, y 76.1 77 78.2 78.8 79.9 81.1 81.8 82.8 Use the p-value method and a 1% significance level to test the claim of linear correlation. How many populations are being tested?
A.   More than two
B.   Two
C.   One
Question #15
Jane wishes to study the relationship between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE). The height is the natural response variable. AGE, x 18 19 21 22 24 25 27 28 H, y 76.1 77 78.2 78.8 79.9 81.1 81.8 82.8 Use the p-value method and a 1% significance level to test the claim of linear correlation. Calculate the sample linear correlation coefficient (round to the nearest ten-thousandth).
A.   0.9633
B.   0.9855
C.   0.9965
D.   0.9145
Question #16
Jane wishes to study the relationship between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE). The height is the natural response variable. AGE, x 18 19 21 22 24 25 27 28 H, y 76.1 77 78.2 78.8 79.9 81.1 81.8 82.8 Use the p-value method and a 1% significance level to test the claim of linear correlation. What is the claim? (At this point, you should have already selected the formula that will be used to calculate the test statistic and written it in the test statistic box.)
A.   ρ > 0
B.   ρ < 0
C.   ρ ≥ 0
D.   ρ = 0
E.   ρ ≠ 0
F.   ρ ≤ 0
Question #17
Jane wishes to study the relationship between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE). The height is the natural response variable. AGE, x 18 19 21 22 24 25 27 28 H, y 76.1 77 78.2 78.8 79.9 81.1 81.8 82.8 Use the p-value method and a 1% significance level to test the claim of linear correlation. The claim is the _________ hypothesis.
A.   null
B.   alternative
Question #18
Jane wishes to study the relationship between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE). The height is the natural response variable. AGE, x 18 19 21 22 24 25 27 28 H, y 76.1 77 78.2 78.8 79.9 81.1 81.8 82.8 Use the p-value method and a 1% significance level to test the claim of linear correlation. What is the alternative hypothesis?
A.   ρ > 0
B.   ρ ≤ 0
C.   ρ ≥ 0
D.   ρ < 0
E.   ρ = 0
F.   ρ ≠ 0
Question #19
Jane wishes to study the relationship between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE). The height is the natural response variable. AGE, x 18 19 21 22 24 25 27 28 H, y 76.1 77 78.2 78.8 79.9 81.1 81.8 82.8 Use the p-value method and a 1% significance level to test the claim of linear correlation. What is the test statistic (rounded to the nearest ten-thousandth)?
A.   28.3673
B.   29.1896
C.   29.3836
D.   29.4521
Question #20
Jane wishes to study the relationship between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE). The height is the natural response variable. AGE, x 18 19 21 22 24 25 27 28 H, y 76.1 77 78.2 78.8 79.9 81.1 81.8 82.8 Use the p-value method and a 1% significance level to test the claim of linear correlation. The critical region is best described as ____________.
A.   right-tailed
B.   left-tailed
C.   two-tailed
Question #21
Jane wishes to study the relationship between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE). The height is the natural response variable. AGE, x 18 19 21 22 24 25 27 28 H, y 76.1 77 78.2 78.8 79.9 81.1 81.8 82.8 Use the p-value method and a 1% significance level to test the claim of linear correlation. What is the smallest upper bound of the p-value from the table (rounded to the nearest thousandth) or the value of the p-value found using technology (rounded to the nearest ten-thousandth?)
A.   0.03
B.   0.01
C.   0.11
D.   0.02
Question #22
Jane wishes to study the relationship between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE). The height is the natural response variable. AGE, x 18 19 21 22 24 25 27 28 H, y 76.1 77 78.2 78.8 79.9 81.1 81.8 82.8 Use the p-value method and a 1% significance level to test the claim of linear correlation. What is the significance level (expressed as a decimal)?
A.   0.01
B.   0.03
C.   0.02
D.   0.11
Question #23
Jane wishes to study the relationship between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE). The height is the natural response variable. AGE, x 18 19 21 22 24 25 27 28 H, y 76.1 77 78.2 78.8 79.9 81.1 81.8 82.8 Use the p-value method and a 1% significance level to test the claim of linear correlation. What is the statistical conclusion?
A.   Reject H0.
B.   Fail to reject H0.
Question #24
Jane wishes to study the relationship between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE). The height is the natural response variable. AGE, x 18 19 21 22 24 25 27 28 H, y 76.1 77 78.2 78.8 79.9 81.1 81.8 82.8 Use the p-value method and a 1% significance level to test the claim of linear correlation. What is the wordy conclusion?
A.   There is not sufficient evidence to warrant rejection of the claim of linear correlation between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE).
B.   There is sufficient evidence to support the claim of linear correlation between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE).
C.   There is not sufficient evidence to support the claim of linear correlation between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE).
D.   There is sufficient evidence to warrant rejection of the claim of linear correlation between the mean heights in centimeters (H) of a group of 161 children in Kalama, an Egyptian village and the groups age in months (AGE).

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