Hw 9.1
9.1 hw 11 The accompanying table shows the height (in inches) of 8 high school girls and their scores on an IQ test. Complete parts (a) through (d) below. Height, x 60 56 64 65 58 64 64 54 IQ score, y 109 98 106 113 93 109 116 128
STAT EDIT LineReg (ax+b) (a) Display the data in a scatter plot STAT EDIT L1 & L2 zoom 9 (see image) (b) Calculate the sample correlation coefficient r STAT CALC 4: LineReg (ax+b) r = -.006 (c) Describe the type of correlation, if any, and interpret the correlation in the context of the data. There is no linear correlation. (d) Interpret the correlation Based on the correlation, there does not appear to be a linear relationship between high school girls' heights and their IQ scores. (e) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let α=0.01. The critical value is .834. Therefore, there is not sufficient evidence at the 1% level of significance to conclude that there is a significant linear correlation between high school girls' heights and their IQ scores.
9.1 hw 13 The accompanying table shows eleven altitudes (in thousands of feet) and the speeds of sound (in feet per second) at these altitudes. Complete parts (a) through (d) below. Altitude, x 0 5 10 15 20 25 30 35 40 45 50 Speed of sound, y 1116.8 1095.8 1077.2 1057.1 1037.4 1016.3 996.3 970.8 967.7 967.7 967.7
STAT EDIT LineReg (ax+b) (a) Display the data in a scatter plot STAT EDIT L1 & L2 zoom 9 (see image) (b) Calculate the sample correlation coefficient r STAT CALC 4: LineReg (ax+b) r = -.974 (c) Describe the type of correlation, if any, and interpret the correlation in the context of the data. There is a strong negative linear correlation. (d) Interpret the correlation As altitude increases, speeds of sound tend to decrease. (e) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let α=0.01. The critical value is .735. Therefore, there is sufficient evidence at the 1% level of significance to conclude that there is a significant linear correlation between altitude and speed of sound.
9.1 hw 12 The accompanying table shows the earnings per share (in dollars) and the dividends per share (in dollars) for 6 companies in a recent year. Complete parts (a) through (d) below. Earnings per share, x 0.96 3.93 3.41 7.97 1.74 2.77 Dividends per share, y 0.95 0.38 2.15 1.02 0.69 1.32
STAT EDIT LineReg (ax+b) (a) Display the data in a scatter plot STAT EDIT L1 & L2 zoom 9 (see image) (b) Calculate the sample correlation coefficient r STAT CALC 4: LineReg (ax+b) r = .024 (c) Describe the type of correlation, if any, and interpret the correlation in the context of the data. There is no linear correlation. (d) Interpret the correlation Based on the correlation, there does not appear to be a linear relationship between companies' earnings per share and their dividends per share (e) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let α=0.01. The critical value is .917. Therefore, there is not sufficient evidence at the 1% level of significance to conclude that there is a significant linear correlation between companies' earnings per share and their dividends per share.
9.1 hw 10 The accompanying table shows the ages (in years) of 11 children and the numbers of words in their vocabulary. Complete parts (a) through (d) below. Age, x 1 2 3 4 5 6 3 5 2 4 6 Vocabulary size, y 5 270 530 1100 1900 2700 560 2100 240 1400 2400
STAT EDIT LineReg (ax+b) (a) Display the data in a scatter plot STAT EDIT L1 & L2 zoom 9 (see image) (b) Calculate the sample correlation coefficient r STAT CALC 4: LineReg (ax+b) r = .978 (c) Describe the type of correlation, if any, and interpret the correlation in the context of the data. There is a strong positive linear correlation. (d) Interpret the correlation As age increases, the number of words in children's vocabulary tends to increase. (e) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let α=0.01. The critical value is .735. Therefore, there is sufficient evidence at the 1% level of significance to conclude that there is a significant linear correlation between children's ages and the number of words in their vocabulary.
9.1 hw 15 The maximum weights (in kilograms) for which one repetition of a half squat can be performed and the times (in seconds) to run a 10-meter sprint for 12 international soccer players are shown in the attached data table with a sample correlation coefficient r of −0.956. A 13th data point was added to the end of the data set for an international soccer player who can perform the half squat with a maximum of 205 kilograms and can sprint 10 meters in 2.01 seconds. Describe how this affects the correlation coefficient r. Use technology Maximum weight, xterm-7 170 175 160 205 155 185 185 155 195 185 160 165 205 Time, y 1.82 1.77 2.06 1.43 2.04 1.61 1.72 1.89 1.59 1.63 1.99 1.92 2.01
STAT EDIT LineReg (ax+b) STAT EDIT L1 & L2 STAT CALC 4: LineReg (ax+b) r = -.657 The new correlation coefficient r gets weaker, going from -0.956 to -.657
9.1 hw 14 The ages (in years) of 10 men and their systolic blood pressures (in millimeters of mercury) are shown in the attached data table with a sample correlation coefficient r of 0.915. Remove the data entry for the man who is 49 years old and has a systolic blood pressure of 199 millimeters of mercury from the data set and find the new correlation coefficient. Describe how this affects the correlation coefficient r. Use technology. Age, x 17 27 37 44 49 63 68 32 57 23 Systolic blood pressure, y 111 122 143 134 199 184 198 132 176 117
STAT EDIT LineReg (ax+b) STAT EDIT L1 & L2 remove 49 & 199 STAT CALC 4: LineReg (ax+b) r = .976 The new correlation coefficient r gets stronger, going from 0.915 to .976
9.1 hw 18 The maximum weights (in kilograms) for which one repetition of a half-squat can be performed and the jump heights (in centimeters) for 12 international soccer players are given in the accompanying table. The correlation coefficient, rounded to three decimal places, is r=0.734. At α=0.05, is there enough evidence to conclude that there is a significant linear correlation between the variables? Maximum weight, x 190 185 155 180 175 170 150 160 160 180 190 210 Jump height, y 61 57 53 59 56 65 51 50 49 58 58 63
STAT EDIT PRGM InvT (custom) LinRegTtest (a) Determine the null and alternative hypotheses. Ho: ρ = 0 Ha: ρ ≠ 0 2 tailed test (b) Identify the critical value(s). Select the correct choice below and fill in any answer boxes within your choice. PRGM InvT AREA LEFT: .025 (.05/2) DF: 10 (n-2) −tₒ = −2.228 and tₒ = 2.228 (c) Calculate the test statistic. STAT TEST E: LinRegTtest (y=a+bx) t = 3.421 (d) Conclusion Reject H0. There is enough evidence at the 5% level of significance to conclude that there is a significant linear correlation between the maximum weight for one repetition of a half squat and the jump height.
9.1 hw 16 The weights (in pounds) of 6 vehicles and the variability of their braking distances (in feet) when stopping on a dry surface are shown in the table. Can you conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry surface? Use α=0.05. Weight, x 5920 5370 6500 5100 5870 4800 Variability in braking distance, y 1.71 1.95 1.91 1.56 1.62 1.50
STAT EDIT PRGM InvT (custom) LinRegTtest (a) Setup the hypothesis for the test. Ho: ρ = 0 Ha: ρ ≠ 0 2 tailed test (b) Identify the critical value(s). PRGM InvT AREA LEFT: .025 (.05/2) DF: 4 (n-2) −tₒ = −2.776 and tₒ = 2.776. (c) Calculate the test statistic. STAT TEST E: LinRegTtest (y=a+bx) t = 1.484 (d) Conclusion There is not enough evidence at the 5% level of significance to conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry surface.
9.1 hw 17 The number of hours 10 students spent studying for a test and their scores on that test are shown in the table. Is there enough evidence to conclude that there is a significant linear correlation between the data? Use α=0.01. Hours, x 0 1 2 4 4 5 5 6 7 8 Test score, y 38 40 55 53 63 66 73 72 81 91
STAT EDIT PRGM InvT (custom) LinRegTtest (a) Setup the hypothesis for the test. Ho: ρ = 0 Ha: ρ ≠ 0 2 tailed test (b) Identify the critical value(s). Select the correct choice below and fill in any answer boxes within your choice. PRGM InvT AREA LEFT: .005 (.01/2) DF: 8 (n-2) −tₒ = −3.355 and tₒ = 3.355. (c) Calculate the test statistic. STAT TEST E: LinRegTtest (y=a+bx) t = 10.65 (d) Conclusion There is enough evidence at the 5% level of significance to conclude that there is a significant linear correlation between hours spent studying and test score.hours spent studying and test score.
