For questions that follow

Unit II Homework Assignment For questions that follow, refer to the following hypothetical data, which lists the pain scores for people treated with the cannabis medicinal in a study targeting adults suffering from peripheral neuropathy(a complication of diabetes mellitus). 90 55 10 45 70 13 27 11 70 14 15 13 75 50 30 80 40 29 13 9 7 20 85 95 1. Compute the sample mean score. (4 points) To calculate the sample mean, add up all the pain scores and divide by the number of scores: (n)/24 = 90 + 55 + 10 + 45 + 70 + 13 + 27 + 11 + 70 + 14 + 15 + 13 + 75 + 50 + 30 + 80 + 40 + 29 + 13 + 9 + 7 + 20 + 85 + 95 = 966 966/24=40.25  Answer: 40.25 2. Compute the sample standard deviation. (4points) To Compute the sample standard deviation, a) Step 1_ Subtract the mean from each data point: Subtract 90 - 40.25 = 49.75 55 - 40.25 = 14.75 10 - 40.25 = 30.25 45 - 40.25 = 4.75 70 - 40.25 = 29.75 13 - 40.25 = -27.25 27 - 40.25 = -13.25 11 - 40.25 = -29.25 70 - 40.25 = 29.75 14 - 40.25 = -26.25 15 - 40.25 = -25.25 13 - 40.25 = -27.25 75 - 40.25 = 34.75 50 - 40.25 = 9.75 30 - 40.25 = -10.25 80 - 40.25 = 39.75 40 - 40.25 = 0.25

29 - 40.25 = -11.25 13 - 40.25 = -27.25 9 - 40.25 = -31.25 7 - 40.25 = -33.25 20- 40.25 = -20.25 85 - 40.25 = 44.75 95 - 40.25 = 54.75 Step 2: Square the deviations above 49.75^2 2475.06 3 14.75^2 217.562 5 30.25^2 915.062 5 4.75^2 22.5625 29.75^2 885.062 5 -27.25^2 742.562 5 -13.25^2 175.562 5 -29.25^2 855.562 5 29.75^2 885.062 5 -26.25^2 689.062 5 -25.25^2 637.562 5 -27.25^2 742.562 5 34.75^2 1207.56 3 9.75^2 95.0625 -10.25^2 105.062 5 39.75^2 1580.06 3 0.25^2 0.0625 -11.25^2 126.562 5 -27.25^2 742.562 5

5 1580.06 3 0.0625 126.562 5 742.562 5 976.562 5 1105.563 410.062 5 2002.56 3 2997.56 3 Sum Total 20592.5 Step 4: Divide the sum by the number of terms (n-1) 20592.5/24-1 =895.3261 Step 5: Take the square root. √895.3261 =29.922 The standard deviation is  Answer 29.922 3. Compute the median score. (4 points) Median score: To find the median score, we need to sort the scores in ascending order and find the middle score. 7, 9,10, 11, 13, 13, 13, 14, 15, 20, 27, 29, 30, 40, 45, 50, 55, 70, 70, 75, 80, 85, 90, 95 There are 24 scores, so the median score is 29, 30, so 29+30=59/2=  Answer= 29.5

4. Compute the first and third quartiles. (4 points)  To find the first quartile, the data must be sorted in ascending order.  Then, Q1 is found by taking the value that is 25% of the way through the data.  If the data has an odd number of values, Q1 is the median of the lower half of the data.  If the data has an even number of values, Q1 is the average of the two middle values in the lower half of the data. 7, 9,10, 11, 13, 13>< 13 , 14, 15, 20, 27, 29 30, 40, 45, 50, 55, 70><70 , 75, 80, 85, 90, 95  1 st quartile= answer 13 To find the third quartile, the data must be sorted in ascending order. Then, Q3 is found by taking the value that is 75% of the way through the data. If the data has an odd number of values, Q3 is the median of the upper half of the data. If the data has an even number of values, Q3 is the average of the two middle values in the upper half of the data.  3 rd Quartile= answer 70 5. What proportion of the sample had higher pain scores (i.e., a pain score of at least 75)? (4points) 5 people had pain scores of 75 and above (75, 80, 85, 90, 95)  n=24  5/24 *100  =20.83% Homework problem #2 (8 points total) The following are summary statistics based on a study to assess the effect of telehealth services on weight monitoring in a sample of 200 patients. n = 200 Mean = 225 Median = 231 Standard deviation = 54 Minimum = 131 Maximum = 320 Q 1 = 179 Q 3 = 266 To determine if there are outliers, one need first to compute the interquartile range. To compute the interquartile range is IQR = Q3 − Q1 1st quartile=179 3rd Quartile=266

Based on the chart, Illinois had the highest proportion of COVID-19 tests performed at 5.2%, followed by Maryland at 2.4%, Arizona at 1.7%, and Vermont with the lowest proportion at 0.4%. Regarding the positivity rate, Vermont had the lowest rate at 4%, followed by Illinois at 6.5%, Maryland at 9.0% and the highest positivity rate was at Arizona at 12.5%. These findings suggest that although Illinois had the highest proportion of COVID-19 tests performed, it had a lower positivity rate than Arizona, which had a lower proportion of COVID- 19 tests performed but a higher positivity rate. On the other hand, Vermont had the lowest proportion of COVID-19 tests performed and the lowest positivity rate. These findings suggest that while a high proportion of COVID-19 tests may indicate a more aggressive approach to testing, it does not necessarily mean a lower positivity rate, as seen in Arizona. Homework problem #4 (62 points total) 8.What is the proportion of mothers who smoke?(4 points) The proportion of mothers is =5/12 or 41.667% 9. What is the mean and standard deviation of baby weight? (8 points) Mean of baby weight 3.2+4.1+2.9+3.0+3.1+2.7+3.3+5.5+3.7+3.4+2.6+4.4=41.9 41.9/12=3.49 Mean=3.49 (answer) Standard Deviation  Step 1_ Subtract the mean from each data point 3.2 - 3.49=-0.29 4.1- 3.49=0.61 2.9- 3.49=-0.59 3.0- 3.49=-0.49 3.1- 3.49=-0.39 2.7- 3.49=-0.79 3.3- 3.49=-0.19 5.5- 3.49=-2.01 3.7- 3.49=-0.21 3.4- 3.49=-0.09 2.6- 3.49=-0.89

4.4- 3.49=0.91 Step 2: Square the deviations above (Squared Deviations) 0.09 0.37 0.35 0.24 0.15 0.63 0.04 4.03 0.04 0.01 0.80 0.83 Next step 3: Sum the squared deviations Sum= 7.57 Divide the sum by the number of terms (n-1) 7.57/12-1=0.69 N : 12 M : 3.49 SS : 7.57 s 2 = SS ⁄( N - 1) = 7.57/(12-1) = 0.69 s = √ s 2 = √0.69 = 0.83 Answer= Standard deviation= 0.83 10. What is the mean and standard deviation of household income? (10 points) Deviation (X - M) Squared Dev 32000 -10458.33 109376736.11 49000 6541.67 42793402.78 22500 -19958.33 398335069.4 4 67000 24541.67 602293402.7 8 37000 -5458.33 29793402.78 47000 4541.67 20626736.11 28000 -14458.33 209043402.7 8 52000 9541.67 91043402.78 45000 2541.67 6460069.44 57000 14541.67 211460069.44

X axis= categories 18-24 25-30 31-34 32-34 35-40 y-axis= frequency count 3 Times 4 Times 2 Times 1 Times 2 Times 18-24 25-30 31-34 32-34 35-40 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 3 4 2 1 2 Frequency 12. Write a summary to include a visual data display of your choosing on the relationship between smoking and a baby’s weight. You may not use a bar chart. (22 points) Smoking during pregnancy has long been associated with an increased risk of adverse outcomes for both mother and baby. One such outcome is low birth weight, which can have severe implications for a newborn’s development and health. From the above hypothetical data smoking mothers gave birth to less heavy babies than mothers who did not smoke. Smoking mothers’ baby weight was an average of 2.86 kgs compared to an average of 3.94 kgs for non-smoking mothers’ babies.

Smoking Mothers Baby Weight Non-Smoking Mothers Baby Weight 2.9 3.2 3.0 4.1 3.1 3.3 2.7 5.5 2.6 3.7 3.4 4.4 Total=14.3kg Average 14.3/5= 2.86kgs Total=27.6 Average 27.6/7 3.94kgs 1 2 3 4 5 0 1 2 3 4 5 6 Chart Title Smoking Mothers Baby Weight Non-Smoking Mothers Baby Weight