Question

Please answer both questions. Will Rate!!

Exposure to microbial products, especially endotoxin, may have an inmpact on vulnerability to allergic diseases. The following are data on concentration (EU/mg) in settled dust for one sample of urban homes and another of farm homes. U: 6.0 5.0 11.0 33.0 4.0 5.0 80.0 18.0 35.0 17.0 23.0 F 3.0 12.0 11.0 6.0 8.0 9.0 3.0 19.0 6.0 9.0 22.0 8.5 4.0 2.0 0.7 each sample. (Round your answers to two decimal places.) the sample mea han bemer EU/mc farm homes Eu/mg How do they compare? OThe average endotoxin concentration urban homes is more than double the average concentration farm homes about the same both urban and farm homes. OThe average endotaxin concentration O The average endotoxin concentration farm homes is more than double the average concentration in urban homes. (b) Determine the sample median for each sample. EU/mg EU/mg How do they compare? OThe median endotoxin concentration in urban homes is roughly double the median concentration farm homes. O The median endotoxin concentration i farm homes is roughly double the median concentration in urban homes. O The median endotoxin concentration is about the same in both urban and farm homes. Why is the median for the urban sample so different from the mean for that sample? OThe mean and median for urban homes are so different because there are fewer observations. The mean and median for urban homes are so different because the measure different aspects of the distribution. OThe mean and median for urban homes are so different because the few large values raise the mean but not the median. (c) Calculate the trimmed mean each sample by deleting the smallest and largest observation. (Round your answers to two decimal places.) EU/mg EU/mg urban homes farm homes What are the corresponding trimming percentages? (Round your answers to two decimal places.) urban homes farm homes % How do the values of these trimmed means compare to the corresponding means and medians? the mean of the entire sample. The trimmed mean is-Select the median of the entire sample. The trimmed mean isSelect- Farm homes: The trimmed mean isSelect- the mean of the entire sample. The trimmed mean is -Select- the median of the entire sample. Human measurements provide a rich area of application for statistical methods. The article "A Longitudinal Study of the Development of Elementary School Children's Private Speech't reported on a study of children talking to themselves (private speech). because IQ is supposed to measure mental maturity, and it was known that private speech decreases as students progress through the primary grades. The study included 33 students whose first- It was thought that private speech would be related to grade I scores are aiven here. 82 96 99 102 103 103 106 107 108 108 108 108 115 118 118 ,18 121 122 122 127 132 136 140 146 Describe the data and comment on any interesting features. (Select all that apply.) The lowest 10, 82, stands ut as a low outlier The distribution of 1Q scores is slightly positively skawed. The distribution of 10 scores is concentrated in the range 106 to 122. The second lowest 1Q, 96, stands out as an outlier. The distribution of IQ scores is symmetric. The distribution of 1O scores is very negatively skewed. The distribution of 10 ceoros is ki. d in the range 100 to 136. highly concentrat scorer o outliars There are

Answer 1

(a) Urban homes 21.55 EU/mg farm homes 8.21 EU/mg The average endotoxin concentration in urban homes is more than double the average concentration in farm homes. (b) Urban homes 17.00 EU/mg farm homes 8.00 EU/mg The median endotoxin concentration in urban homes is roughly double the median concentration in farm homes. The mean and median for urban homes raise the mean but not the median (c) Urban homes 17.00 EU /mg different because the few large values are so 7.73 EU mg Farm homes Urban homes (1/11) 100 9.09% Farm homes (1/15) 100 6.67% Urban homes _ The trimmed mean is smal ler than the mean of the entire sample. The trimmed mean is same as the median of the entire sample. Farm homes The trimmed mean is smal ler than the mean smaller than the median of the entire sample. of the entire sample. The trimmed mean is

Problem 2:

Variable Mean Minimum Q1 Median Q3 Maximum IQR
IQ 113.73 82.00 107.50 113.00 120.00 146.00 12.50

Lower whisker=Q1-1.5IQR=107.50-1.5*12.50=88.75, Upper whisker=Q3+1.5IQR=120+1.5*12.50=138.75

Since any value lies outside the interval [88.75, 138.75] is treated as outlier.

Hence The lowest IQ is 82, stands out as a low outlier.

Since Median-Q1=113-107.50=5.5<Q3-Median=120-113=7 so

The distribution of IQ scores is slightly positively skewed.