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A study in a journal published by the American Academy of Pediatrics (as reported in the Miami Herald, Jan. 14, 1997) seems to suggest that preschoolers who drink more than 12 ounces of fruit juice a day tend to be heavier and shorter than preschoolers who do not.  The study involved a random sample of 168 healthy youngsters of whom 59 drank on average more than 12 ounces of fruit juice per day.  Each child was weighed and measured.  The measurements were then converted to percentage of normal height and weight for a child of that age and gender.  For example, a weight percentage of 1.1 indicates that the child is 10% heavier than average. A recorded 0.80 indicates the child is 20% below the average.  An average weight is recorded as 1.0.  Same with height. Column 1:         Juice                1- indicates child DID drink > 12 oz                                                       2- child DID NOT drink > 12 oz Column 2:         Weight%          weight converted to percent of average (see description above) Column 3:         Height%           height converted to percent of average (see description above) 1. Assuming this random sample is representative of all pre-schoolers, estimate the percentage of pre-schoolers at risk for consuming more than 12 ounces of juice per day and construct a 95% confidence interval to account for the margin of error of this sample.

A study in a journal published by the American Academy of Pediatrics (as reported in the Miami Herald, Jan. 14, 1997) seems to suggest that preschoolers who drink more than 12 ounces of fruit juice a day tend to be heavier and shorter than preschoolers who do not.  The study involved a random sample of 168 healthy youngsters of whom 59 drank on average more than 12 ounces of fruit juice per day.  Each child was weighed and measured.  The measurements were then converted to percentage of normal height and weight for a child of that age and gender.  For example, a weight percentage of 1.1 indicates that the child is 10% heavier than average. A recorded 0.80 indicates the child is 20% below the average.  An average weight is recorded as 1.0.  Same with height. Column 1:         Juice                1- indicates child DID drink > 12 oz                                                       2- child DID NOT drink > 12 oz Column 2:         Weight%          weight converted to percent of average (see description above) Column 3:         Height%           height converted to percent of average (see description above) 1. Assuming this random sample is representative of all pre-schoolers, estimate the percentage of pre-schoolers at risk for consuming more than 12 ounces of juice per day and construct a 95% confidence interval to account for the margin of error of this sample.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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A study in a journal published by the American Academy of Pediatrics (as reported in the Miami Herald, Jan. 14, 1997) seems to suggest that preschoolers who drink more than 12 ounces of fruit juice a day tend to be heavier and shorter than preschoolers who do not.  The study involved a random sample of 168 healthy youngsters of whom 59 drank on average more than 12 ounces of fruit juice per day.  Each child was weighed and measured.  The measurements were then converted to percentage of normal height and weight for a child of that age and gender.  For example, a weight percentage of 1.1 indicates that the child is 10% heavier than average. A recorded 0.80 indicates the child is 20% below the average.  An average weight is recorded as 1.0.  Same with height.

Column 1:         Juice                1- indicates child DID drink > 12 oz      

                                                2- child DID NOT drink > 12 oz

Column 2:         Weight%          weight converted to percent of average (see description above)

Column 3:         Height%           height converted to percent of average (see description above)

1. Assuming this random sample is representative of all pre-schoolers, estimate the percentage of pre-schoolers at risk for consuming more than 12 ounces of juice per day and construct a 95% confidence interval to account for the margin of error of this sample.

Data:

Juice Weight% Height%
1 0.88 0.88
1 1.2 1.09
1 1.22 0.87
1 1.1 1
1 0.87 0.95
1 1.18 0.72
1 0.96 1.04
1 1.06 0.87
1 1.01 0.99
1 0.94 1.16
1 1.27 1.06
1 0.82 1.04
1 0.9 0.95
1 1 1.07
1 1.02 1.09
1 1.07 1.05
1 0.99 0.88
1 0.98 1.1
1 0.95 0.91
1 1.05 1.08
1 1.02 0.87
1 1.02 1
1 1.21 0.97
1 1.11 1.02
1 1.02 0.92
1 0.84 0.88
1 1.02 0.98
1 1.04 1.01
1 1.2 0.98
1 1.23 1.11
1 0.97 0.85
1 1.01 1.04
1 1.26 0.86
1 1.14 0.95
1 0.89 0.99
1 0.88 0.93
1 0.99 0.88
1 1.12 0.91
1 0.93 0.94
1 1.13 0.99
1 1.03 1.03
1 1.04 0.84
1 0.97 0.91
1 0.96 0.76
1 0.89 0.99
1 1.11 0.98
1 1.09 0.7
1 0.91 1.08
1 1.01 0.92
1 1.12 1.09
1 1.06 0.82
1 1.2 0.86
1 1.23 0.77
1 1.09 1.02
1 0.95 0.87
1 1 0.92
1 1.12 1.02
1 0.99 0.83
1 0.96 0.92
2 0.88 1.14
2 0.92 1.02
2 1.02 0.95
2 0.83 0.93
2 0.87 1.19
2 0.93 0.89
2 0.92 0.91
2 1.07 0.8
2 1 0.91
2 0.92 1.01
2 0.83 0.99
2 0.89 1.1
2 1.07 0.91
2 1.04 1.13
2 1.1 1.13
2 0.86 0.91
2 1.1 1.04
2 0.93 0.9
2 1.01 0.96
2 0.94 1.05
2 1.03 0.92
2 1.02 1.07
2 1.06 1.27
2 0.94 0.99
2 0.93 1.17
2 1.06 1.07
2 1.09 0.89
2 1.12 0.99
2 0.72 0.93
2 1.07 0.94
2 0.96 1.13
2 0.95 0.91
2 0.96 1.06
2 1.08 1.03
2 0.93 1.08
2 1.05 1.01
2 1 0.83
2 0.95 0.99
2 1.12 1.05
2 0.99 0.84
2 1.07 0.99
2 0.99 1.1
2 1.04 1.11
2 0.98 1.02
2 1.03 1.01
2 0.98 0.88
2 1.06 1.07
2 0.91 1.07
2 0.85 1.02
2 0.85 0.97
2 0.86 0.94
2 1 0.93
2 0.94 0.94
2 0.87 1.03
2 1.04 0.99
2 0.95 0.99
2 1.04 1
2 1.05 1.01
2 0.99 0.98
2 0.95 0.97
2 1 1.1
2 0.98 1.09
2 1.11 0.97
2 0.82 0.9
2 0.97 1.17
2 0.87 0.87
2 1.01 1.11
2 0.92 0.95
2 0.84 0.95
2 1.16 1
2 0.9 1.15
2 1.14 0.92
2 1.15 1.06
2 1.05 0.83
2 1.01 1.22
2 0.9 0.99
2 1.04 1.25
2 1.03 0.96
2 0.88 1
2 1.11 1.06
2 0.95 1
2 0.97 1.09
2 0.92 0.93
2 0.73 0.98
2 1.01 0.98
2 0.98 0.86
2 0.98 0.91
2 1.02 0.96
2 1.02 1.1
2 1.05 0.89
2 0.79 0.93
2 0.99 0.86
2 1.2 1.16
2 0.93 0.98
2 0.97 1.04
2 1.05 0.98
2 0.93 0.96
2 1.08 1
2 0.93 1.1
2 0.84 1.11
2 1.03 0.99
2 1.19 1.01
2 0.92 0.86
2 0.85 0.87
2 1.01 1.03
2 1.12 1.03
2 0.83 1.07
2 1.11 1.06
2 0.96 1.04
Weight%Yes Weight%No Height %No Height%Yes Мean 1.0378 0.9804 Mean 1.0036 0.9527 Variance 0.0125 0.0090 Varian ce 0.0089 0.0102 Observations 59 109 Observations 109 59 Pooled Variance 0.0103 Pooled Variance 0.0094 Hypothesized Mean Differen ce Hypothesized Mean Difference df 166 df 166 t Stat t Stat P(T<=t) one-tail t Critical one-tail P(T<t) two-tail 3.5095 3.2543 P(T<=t) one-tail 0.0003 0.0007 tCritical one-tail 1.6541 1.6541 P(T<=t) two-tail 0.0006 0.0014 t Critical two-tail 1.9744 t Critical two-tail 1.974
Transcribed Image Text:Weight%Yes Weight%No Height %No Height%Yes Мean 1.0378 0.9804 Mean 1.0036 0.9527 Variance 0.0125 0.0090 Varian ce 0.0089 0.0102 Observations 59 109 Observations 109 59 Pooled Variance 0.0103 Pooled Variance 0.0094 Hypothesized Mean Differen ce Hypothesized Mean Difference df 166 df 166 t Stat t Stat P(T<=t) one-tail t Critical one-tail P(T<t) two-tail 3.5095 3.2543 P(T<=t) one-tail 0.0003 0.0007 tCritical one-tail 1.6541 1.6541 P(T<=t) two-tail 0.0006 0.0014 t Critical two-tail 1.9744 t Critical two-tail 1.974
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