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 ozColumn 2: Weight% weight converted to percent of average (see description above)Column 3: Height% height converted to percent of average (see description above) 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. 59/168 = 0.35 -> 35%alpha = 0.05 Data:JuiceWeight%Height%10.880.8811.21.0911.220.8711.1110.870.9511.180.7210.961.0411.060.8711.010.9910.941.1611.271.0610.821.0410.90.95111.0711.021.0911.071.0510.990.8810.981.110.950.9111.051.0811.020.8711.02111.210.9711.111.0211.020.9210.840.8811.020.9811.041.0111.20.9811.231.1110.970.8511.011.0411.260.8611.140.9510.890.9910.880.9310.990.8811.120.9110.930.9411.130.9911.031.0311.040.8410.970.9110.960.7610.890.9911.110.9811.090.710.911.0811.010.9211.121.0911.060.8211.20.8611.230.7711.091.0210.950.87110.9211.121.0210.990.8310.960.9220.881.1420.921.0221.020.9520.830.9320.871.1920.930.8920.920.9121.070.8210.9120.921.0120.830.9920.891.121.070.9121.041.1321.11.1320.860.9121.11.0420.930.921.010.9620.941.0521.030.9221.021.0721.061.2720.940.9920.931.1721.061.0721.090.8921.120.9920.720.9321.070.9420.961.1320.950.9120.961.0621.081.0320.931.0821.051.01210.8320.950.9921.121.0520.990.8421.070.9920.991.121.041.1120.981.0221.031.0120.980.8821.061.0720.911.0720.851.0220.850.9720.860.94210.9320.940.9420.871.0321.040.9920.950.9921.04121.051.0120.990.9820.950.97211.120.981.0921.110.9720.820.920.971.1720.870.8721.011.1120.920.9520.840.9521.16120.91.1521.140.9221.151.0621.050.8321.011.2220.90.9921.041.2521.030.9620.88121.111.0620.95120.971.0920.920.9320.730.9821.010.9820.980.8620.980.9121.020.9621.021.121.050.8920.790.9320.990.8621.21.1620.930.9820.971.0421.050.9820.930.9621.08120.931.120.841.1121.030.9921.191.0120.920.8620.850.8721.011.0321.121.0320.831.0721.111.0620.961.04 Weight%Yes Weight%NoHeight %No Height%YesМean1.03780.9804Mean1.00360.9527Variance0.01250.0090Varian ce0.00890.0102Observations59109Observations10959Pooled Variance0.0103Pooled Variance0.0094Hypothesized Mean Differen ceHypothesized Mean Differencedf166df166t Statt StatP(T<=t) one-tailt Critical one-tailP(T

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Description: 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 preschoole

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)

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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)

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.

59/168 = 0.35 -> 35%
alpha = 0.05

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

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