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Descriptive Statistics,Confdence Interval&Hypothesis Testing

1. Analyze that data set:
For this part, if you are male use the male variable; if you are female use the female variable.
a. Determine the center of the data using the mean, mode, and median.
b. Determine measures of variation (range, standard deviation and variance).
c. Determine the quartiles.
d. Determine the IQR (Inner Quartile Range) and any outliers in the data.
e. Create the modified boxplot of the data showing any outliers. (You may need to draw this using MS Word tools.). Make sure that your boxplot has a proper scale.
f. Using Excel, group the data into 6 to 10 groups and create a histogram for the data. (Excel uses bins to group the data. See the attached worksheet for instructions on creating the histogram.)
2. Draw inferences from the data. (For the last part of this section you will need to use both male and female data for your variable.)
a. Use the sample data to construct a 90% confidence interval for the mean of all males or females.
b. Use the sample data to construct a 98% confidence interval for the mean of all males or females.
c. Test the hypothesis that the mean of all males is the same as the mean of all females for your variable.
3. Write a formal paper incorporating and explaining the results in steps two and three above.
a. Include an introduction, body, and conclusions.
b. Describe how you would collect the sample data you are using. Be sure to use the sampling methods you have learned in your discussion as well as the random process in Excel.
c. Include an explanation of any problems that might occur when collecting this data. (E.g., if the data was "finger length" you might discuss which finger is chosen, whether to include the nail and knuckle, rounding errors, etc.)
d. Describe and give the measures of the center and explain which measure best fits this data set.
e. Describe and give the measures of variation.
f. Include the boxplot, showing outliers, with an explanation of how outliers are determined. Give the quartiles and IQR in this explanation.
g. Discuss the standard deviation of the data set.
? Determine the ACTUAL percent of your data set that is within one, two, and three standard deviations of the sample mean.
? Compare these results to Chebyshev's rule.
? Compare these results to the empirical rule.
? Explain any conflict with your data and both of these two rules.
h. Include the histogram of the data and a description of the shape of the distribution.
i. Include the boxplot along with an explanation of what it tells you about the distribution of your data.
j. Include the two confidence intervals.
? Explain the purpose of a confidence interval.
? Include the requirements check.
? Explain which interval is larger and why.
? Interpret the results of both intervlas.
k. Conduct a test of the hypothesis that the mean of all males is the same as the mean of all of all females for your variable.
? Include the two hypotheses.
? Explain how the requirements are met.
? Give the level of significance used, the test statistic, and the p-value.
? State the decision.
? Interpret the results
MALE AGE HT WT WAIST PULSE SYS DIAS CHOL BMI LEG ELBOW WRIST ARM
1391 58 70.8 169.1 90.6 68 125 78 522 23.8 42.5 7.7 6.4 31.9
2129 22 66.2 144.2 78.1 64 107 54 127 23.2 40.2 7.6 6.2 31.0
2489 32 71.7 179.3 96.5 88 126 81 740 24.6 44.4 7.3 5.8 32.7
2490 31 68.7 175.8 87.7 72 110 68 49 26.2 42.8 7.5 5.9 33.4
2738 28 67.6 152.6 87.1 64 110 66 230 23.5 40.0 7.1 6.0 30.1
2988 46 69.2 166.8 92.4 72 107 83 316 24.5 47.3 7.1 5.8 30.5
2989 41 66.5 135.0 78.8 60 113 71 590 21.5 43.4 6.5 5.2 27.6
3346 56 67.2 201.5 103.3 88 126 72 466 31.4 40.1 7.5 5.6 38.0
3606 20 68.3 175.2 89.1 76 137 85 121 26.4 42.1 7.5 5.5 32.0
3607 54 65.6 139.0 82.5 60 110 71 578 22.7 36.0 6.9 5.5 29.3
3608 17 63.0 156.3 86.7 96 109 65 78 27.8 44.2 7.1 5.3 31.7
3610 73 68.3 186.6 103.3 72 153 87 265 28.1 36.7 8.1 6.7 30.7
3747 52 73.1 191.1 91.8 56 112 77 250 25.2 48.4 8.0 5.2 34.7
4832 25 67.6 151.3 75.6 64 119 81 265 23.3 41.0 7.0 5.7 30.6
4839 29 68.0 209.4 105.5 60 113 82 273 31.9 39.8 6.9 6.0 34.2
5599 17 71.0 237.1 108.7 64 125 76 272 33.1 45.2 8.3 6.6 41.1
5600 41 61.3 176.7 104.0 84 131 80 972 33.2 40.2 6.7 5.7 33.1
5601 52 76.2 220.6 103.0 76 121 75 75 26.7 46.2 7.9 6.0 32.2
6226 32 66.3 166.1 91.3 84 132 81 138 26.6 39.0 7.5 5.7 31.2
7190 20 69.7 137.4 75.2 88 112 44 139 19.9 44.8 6.9 5.6 25.9
7192 20 65.4 164.2 87.7 72 121 65 638 27.1 40.9 7.0 5.6 33.7
7194 29 70.0 162.4 77.0 56 116 64 613 23.4 43.1 7.5 5.2 30.3
9073 18 62.9 151.8 85.0 68 95 58 762 27.0 38.0 7.4 5.8 32.8
9074 26 68.5 144.1 79.6 64 110 70 303 21.6 41.0 6.8 5.7 31.0
10864 33 68.3 204.6 103.8 60 110 66 690 30.9 46.0 7.4 6.1 36.2
12349 55 69.4 193.8 103.0 68 125 82 31 28.3 41.4 7.2 6.0 33.6
15515 53 69.2 172.9 97.1 60 124 79 189 25.5 42.7 6.6 5.9 31.9
16137 28 68.0 161.9 86.9 60 131 69 957 24.6 40.5 7.3 5.7 32.9
16521 28 71.9 174.8 88.0 56 109 64 339 23.8 44.2 7.8 6.0 30.9
16523 37 66.1 169.8 91.5 84 112 79 416 27.4 41.8 7.0 6.1 34.0
16768 40 72.4 213.3 102.9 72 127 72 120 28.7 47.2 7.5 5.9 34.8
17006 33 73.0 198.0 93.1 84 132 74 702 26.2 48.2 7.8 6.0 33.6
18392 26 68.0 173.3 98.9 88 116 81 1252 26.4 42.9 6.7 5.8 31.3
19017 53 68.7 214.5 107.5 56 125 84 288 32.1 42.8 8.2 5.9 37.6
19381 36 70.3 137.1 81.6 64 112 77 176 19.6 40.8 7.1 5.3 27.9
19635 34 63.7 119.5 75.7 56 125 77 277 20.7 42.6 6.6 5.3 26.9
19991 42 71.1 189.1 95.0 56 120 83 649 26.3 44.9 7.4 6.0 36.9
20518 18 65.6 164.7 91.1 60 118 68 113 26.9 41.1 7.0 6.1 34.5
21135 44 68.3 170.1 94.9 64 115 75 656 25.6 44.5 7.3 5.8 32.1
32230 20 66.3 151.0 79.9 72 115 65 172 24.2 44.0 7.1 5.4 30.7

Notes: Age in years 49
HT: height in inches 5'10''
WT: weight in pounds 190
WAIST: waist circumference in cm 36
PULSE: pulse rate in beats per minute 65
SYS: systolic blood pressure in mmHg 89/90
DIAS: diastolic blood pressure in mmHg
CHOL: cholesterol in mg 253
BMI: body mass index
LEG: upper leg length in cm
ELBOW: elbow breadth in cm
WRIST: wrist breadth in cm
ARM: arm circumference in cm

Credit: U.S. Department of Health and Human Services.
National Center for Health Statistics
Third National Health and Nutrition Examination Survey.

***delete the first column of ID numbers***

FEMALE AGE HT WT WAIST PULSE SYS DIAS CHOL BMI LEG ELBOW WRIST ARM
295 17 64.3 114.8 67.2 76 104 61 264 19.6 41.6 6.0 4.6 23.6
2739 32 66.4 149.3 82.5 72 99 64 181 23.8 42.8 6.7 5.5 26.3
2992 25 62.3 107.8 66.7 88 102 65 267 19.6 39.0 5.7 4.6 26.3
3745 55 62.3 160.1 93.0 60 114 76 384 29.1 40.2 6.2 5.0 32.6
4486 27 59.6 127.1 82.6 72 94 58 98 25.2 36.2 5.5 4.8 29.2
4488 29 63.6 123.1 75.4 68 101 66 62 21.4 43.2 6.0 4.9 26.4
4878 25 59.8 111.7 73.6 80 108 61 126 22.0 38.7 5.7 5.1 27.9
4880 12 63.3 156.3 81.4 64 104 41 89 27.5 41.0 6.8 5.5 33.0
4881 41 67.9 218.8 99.4 68 123 72 531 33.5 43.8 7.8 5.8 38.6
4835 32 61.4 110.2 67.7 68 93 61 130 20.6 37.3 6.3 5.0 26.5
4842 31 66.7 188.3 100.7 80 89 56 175 29.9 42.3 6.6 5.2 34.4
6225 19 64.8 105.4 72.9 76 112 62 44 17.7 39.1 5.7 4.8 23.7
8680 19 63.1 136.1 85.0 68 107 48 8 24.0 40.3 6.6 5.1 28.4
8681 23 66.7 182.4 85.7 72 116 62 112 28.9 48.6 7.2 5.6 34.0
12348 40 66.8 238.4 126.0 96 181 102 462 37.7 33.2 7.0 5.4 35.2
14651 23 64.7 108.8 74.5 72 98 61 62 18.3 43.4 6.2 5.2 24.7
16767 27 65.1 119.0 74.5 68 100 53 98 19.8 41.5 6.3 5.3 27.0
17765 45 61.9 161.9 94.0 72 127 74 447 29.8 40.0 6.8 5.0 35.0
19377 41 64.3 174.1 92.8 64 107 67 125 29.7 38.2 6.8 4.7 33.1
19378 56 63.4 181.2 105.5 80 116 71 318 31.7 38.2 6.9 5.4 39.6
19382 22 60.7 124.3 75.5 64 97 64 325 23.8 38.2 5.9 5.0 27.0
20278 57 63.4 255.9 126.5 80 155 85 600 44.9 41.0 8.0 5.6 43.8
21626 24 62.6 106.7 70.0 76 106 59 237 19.2 38.1 6.1 5.0 23.6
32233 37 60.6 149.9 98.0 76 110 70 173 28.7 38.0 7.0 5.1 34.3
33104 59 63.5 163.1 104.7 76 105 69 309 28.5 36.0 6.7 5.1 34.4
33106 40 58.6 94.3 67.8 80 118 82 94 19.3 32.1 5.4 4.2 23.3
33334 45 60.2 159.7 99.3 104 133 83 280 31.0 31.1 6.4 5.2 35.6
33335 52 67.6 162.8 91.1 88 113 75 254 25.1 39.4 7.1 5.3 31.8
34779 31 63.4 130.0 74.5 60 113 66 123 22.8 40.2 5.9 5.1 27.0
35035 32 64.1 179.9 95.5 76 107 67 596 30.9 39.2 6.2 5.0 32.8
35272 23 62.7 147.8 79.5 72 95 59 301 26.5 39.0 6.3 4.9 31.0
35273 23 61.3 112.9 69.1 72 108 72 223 21.2 36.6 5.9 4.7 27.0
35505 47 58.2 195.6 105.5 88 114 79 293 40.6 27.0 7.5 5.5 41.2
35506 36 63.2 124.2 78.8 80 104 73 146 21.9 38.5 5.6 4.7 25.5
35507 34 60.5 135.0 85.7 60 125 73 149 26.0 39.9 6.4 5.2 30.9
35984 37 65.0 141.4 92.8 72 124 85 149 23.5 37.5 6.1 4.8 27.9
35988 18 61.8 123.9 72.7 88 92 46 920 22.8 39.7 5.8 5.0 26.5
36115 29 68.0 135.5 75.9 88 119 81 271 20.7 39.0 6.3 4.9 27.8
36502 48 67.0 130.4 68.6 124 93 64 207 20.5 41.6 6.0 5.3 23.0
38089 16 57.0 100.7 68.7 64 106 64 2 21.9 33.8 5.6 4.6 26.4

Please see attached.

Attachments

Solution Summary

The solution provides step by step method for the calculation of descriptive statistics, confidence interval and testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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