Recall in our discussion of the normal distribution the research study that examined the blood vitamin D levels of the entire US population of landscape gardeners. The intent of this large-scale and comprehensive study was to characterize fully this population of landscapers as normally distributed with a corresponding population mean and standard deviation, which were determined from the data collection of the entire population.

Suppose you are now in a different reality in which this study never took place though you are still interested in studying the average vitamin D levels of US landscapers. In other words, the underlying population mean and standard deviation are now unknown to you. You obtain research funding to randomly sample 11 landscapers, collect blood samples, and send these samples to your collaborating lab in order to quantify the amount of vitamin D in the landscapers' blood. After anxiously awaiting your colleagues to complete their lab quantification protocol, they email you the following vitamin D level data as shown in the following table.

SubjectVitamin D134.281234.748339.383435.428540.486642.767728.160836.289936.0291041.2851134.837What is the estimated 95% confidence interval (CI) of the average blood vitamin D level of US landscapers in ng/mL?

Please note the following: 1) you might calculate a CI that is different from any of the multiple choice options listed below due to rounding differences, therefore select the closest match; 2) ensure you use either the large or small sample CI formula as appropriate; and 3) you may copy and paste the data into Excel to facilitate analysis.

Select one:

a.

33.9 to 39.5 ng/mL

b.

29.5 to 44.6 ng/mL

c.

37.2 to 45.6 ng/mL

d.

31.6 to 42.2 ng/mL

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Recall in our discussion of the normal distribution the research study that examined the blood vitamin D levels of the entire US population of landscape gardeners. The intent of this large-scale and comprehensive study was to characterize fully this population of landscapers as normally distributed with a corresponding population mean and standard deviation, which were determined from the data collection of the entire population.

Suppose you are now in a different reality in which this study never took place though you are still interested in studying the average vitamin D levels of US landscapers. In other words, the underlying population mean and standard deviation are now unknown to you. Furthermore, you would like to collect data from US office workers to examine the difference between the average vitamin D levels of landscapers and office workers, which will reflect any occupational sun exposure differences as measured by blood vitamin D levels. You obtain research funding to sample at random 12 landscapers and 14 office workers, collect blood samples, and send these samples to your collaborating lab in order to quantify the amount of vitamin D in both groups' blood. After anxiously awaiting your colleagues to complete their lab quantification protocol, they email you the following vitamin D level data as shown in the following tables.

Table 1. LandscapersSubjectVitamin D152.628245.287343.800438.425541.850642.634744.018835.564939.9091053.8231152.8611255.240Table 2. Office WorkersSubjectVitamin D134.703235.743335.161424.250535.726629.180721.064828.445929.0951028.2391131.1291243.6671338.7811431.149What is the estimated 95% confidence interval (CI) of the average difference in blood vitamin D levels between US landscapers and office workers in ng/mL? Assign groups 1 and 2 to be landscapers and office workers, respectively.

Please note the following: 1) in practice, you as the analyst decide how to assign groups 1 and 2 and subsequently interpret the results appropriately in the context of the data, though for the purposes of this exercise the groups are assigned for you; 2) you might calculate a CI that is different from any of the multiple choice options listed below due to rounding differences, therefore select the closest match; 3) ensure you use either the large or small sample CI formula as appropriate; and 4) you may copy and paste the data into Excel to facilitate analysis.

Select one:

a.

9.18 to 19.98 ng/mL

b.

9.13 to 21.56 ng/mL

c.

8.58 to 18.67 ng/mL

d.

7.20 to 20.16 ng/mL

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Recall in our discussion of the binomial distribution the research study that examined schoolchildren developing nausea and vomiting following holiday parties. The intent of this study was to calculate probabilities corresponding to a specified number of children becoming sick out of a given sample size. Recall also that the probability, i.e. the binomial parameter "p" defined as the probability of "success" for any individual, of a randomly selected schoolchild becoming sick was given.

Suppose you are now in a different reality, in which this binomial probability parameterpis now unknown to you but you are still interested in carrying out the original study described above, though you must first estimatepwith a certain level of confidence. Furthermore, you would also like to collect data from adults to examine the difference between the proportion with nausea and vomiting following holiday parties of schoolchildren and adults, which will reflect any possible age differences in becoming sick. You obtain research funding to randomly sample 48 schoolchildren and 30 adults with an inclusion criterion that a given participant must have recently attended a holiday party, and conduct a medical evaluation by a certified pediatrician and general practitioner for the schoolchildren and adults, respectively. After anxiously awaiting your medical colleagues to complete their medical assessments, they email you data contained in the following tables.

Table 1. SchoolchildrenSubjectNausea and

Vomiting?102031405060708090101110120130140150160170180190200211220230241250260270280290300310321330340350360370380391400410421430440450460470480Table 2. AdultsSubjectNausea and

Vomiting?112030415060708090101110120130140150160170180190200210220231240250260270280291300What is the estimated 95% confidence interval (CI) of the difference in proportions between schoolchildren and adults developing nausea and vomiting following holiday parties? Assign groups 1 and 2 to be schoolchildren and adults, respectively.

Please note the following: 1) in practice, you as the analyst decide how to assign groups 1 and 2 and subsequently interpret the results appropriately in the context of the data, though for the purposes of this exercise the groups are assigned for you; 2) 0 and 1 are defined as no and yes, respectively, which is a typical coding scheme in Public Health; 3) you might calculate a CI that is different from any of the multiple choice options listed below due to rounding differences, therefore select the closest match; and 4) you may copy and paste the data into Excel to facilitate analysis.

Select one:

a.

-0.2015 to 0.1640

b.

-0.2155 to 0.1239

c.

-0.2174 to 0.1647

d.

-0.1874 to 0.1458

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Recall in our discussion of the normal distribution the research study that examined the blood vitamin D levels of the entire US population of landscape gardeners. The intent of this large-scale and comprehensive study was to characterize fully this population of landscapers as normally distributed with a corresponding population mean and standard deviation, which were determined from the data collection of the entire population.

Suppose you are now in a different reality in which this study never took place though you are still interested in studying the average vitamin D levels of US landscapers. In other words, the underlying population mean and standard deviation are now unknown to you. Furthermore, you would like to collect data from US office workers to examine the difference between the average vitamin D levels of landscapers and office workers, which will reflect any occupational sun exposure differences as measured by blood vitamin D levels. You obtain research funding to sample at random 44 landscapers and 48 office workers, collect blood samples, and send these samples to your collaborating lab in order to quantify the amount of vitamin D in both groups' blood. After anxiously awaiting your colleagues to complete their lab quantification protocol, they email you the following vitamin D level data as shown in the following tables.

Table 1. LandscapersSubjectVitamin D147.518237.620341.544442.613539.343639.714741.109832.133939.2611034.5951138.6291238.7091345.0761438.9961540.2231636.1591743.5971832.2991935.9742033.1472130.3802223.9792338.9652438.2352543.8962639.9082727.3642838.6922931.9783047.3403128.2083232.7533343.7543438.4893541.7173635.0563739.5653836.5193934.0024027.5824127.8144225.8064349.1484449.757Table 2. Office WorkersSubjectVitamin D132.546239.397333.777440.381546.354648.642737.293841.081939.0921039.0171140.3021237.6191341.3131444.9281538.9491633.3991736.0851828.8411935.1042036.3842143.7332237.0712339.1362440.1502536.5302645.4222737.8692847.6472938.8813043.8993137.7583243.6153339.0223446.6513534.3163634.8553730.5243835.6083942.3464030.8744130.4544236.6384334.6574445.6774540.2474639.0204734.2274839.594What is the estimated 95% confidence interval (CI) of the average difference in blood vitamin D levels between US landscapers and office workers in ng/mL? Assign groups 1 and 2 to be landscapers and office workers, respectively.

Please note the following: 1) in practice, you as the analyst decide how to assign groups 1 and 2 and subsequently interpret the results appropriately in the context of the data, though for the purposes of this exercise the groups are assigned for you; 2) you might calculate a CI that is different from any of the multiple choice options listed below due to rounding differences, therefore select the closest match; 3) ensure you use either the large or small sample CI formula as appropriate; and 4) you may copy and paste the data into Excel to facilitate analysis.

Select one:

a.

-3.89 to 1.13 ng/mL

b.

-3.46 to 1.05 ng/mL

c.

-3.22 to 1.15 ng/mL

d.

-3.84 to 1.16 ng/mL

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Question5

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Recall in our discussion of the normal distribution the research study that examined the blood vitamin D levels of the entire US population of landscape gardeners. The intent of this large-scale and comprehensive study was to characterize fully this population of landscapers as normally distributed with a corresponding population mean and standard deviation, which were determined from the data collection of the entire population.

Suppose you are now in a different reality in which this study never took place though you are still interested in studying the average vitamin D levels of US landscapers. In other words, the underlying population mean and standard deviation are now unknown to you. Furthermore, you would like to examine if wearing tank tops instead of short sleeve shirts significantly effects vitamin D levels. To accomplish this, you propose to collect data from the landscapers at two different points in time. Specifically, the landscapers are to wear short sleeve shirts while outside working during a period of three weeks. After three weeks, you collect blood specimens and the landscapers are then to wear tank tops for the next three weeks under the same working conditions, after which you collect blood draws a second time. You obtain research funding to randomly sample 48 landscapers, collect blood samples at two different time points as described above, and send these samples to your collaborating lab in order to quantify the amount of vitamin D in the landscapers' blood. After anxiously awaiting your colleagues to complete their lab quantification protocol, they email you the following vitamin D level data as shown in the following table.

SubjectTime Point 1, Shirts

Vitamin D (ng/mL)Time Point 2, Tank Tops

Vitamin D (ng/mL)151.19439.914241.44239.010349.15435.538442.66531.920546.24234.011653.16132.438743.66729.840843.99131.336943.80238.1081044.14339.8091140.81844.6981235.90431.7891355.02638.5431446.68931.5621541.21030.4181653.06534.8951746.81633.4851841.57138.8171942.25237.2102047.78831.8792133.62536.0462252.58838.0692351.80637.6992438.27232.8162551.50935.8532647.42448.5382747.34332.5102856.65335.8582947.71939.5503044.36740.4163140.61735.1493236.06333.2053344.93238.9443445.33631.5613553.12741.3753644.07041.5003749.21535.5143854.54840.1973936.37538.5024036.42935.7334147.52933.9904256.79846.6404340.83138.2284451.58228.4644552.53038.9774647.93039.4574754.91836.6094843.01438.386What is the estimated 95% confidence interval (CI) of the average difference in blood vitamin D levels between short sleeve shirt and tank top attire amongst US landscapers in ng/mL?

Please note the following: 1) in practice, you as the analyst decide how to calculate the difference in vitamin D levels between time points for a given study participant, and subsequently interpret the aggregated results appropriately in the context of the data, though for the purposes of this exercise the difference is assigned for you as follows.Define the difference as the second minus the first time points, which is common practice, since the plus or minus sign of the resulting difference reflects any change over sequential time; 2) you might calculate a CI that is different from any of the multiple choice options listed below due to rounding differences, therefore select the closest match; 3) ensure you use either the large or small sample CI formula as appropriate; and 4) you may copy and paste the data into Excel to facilitate analysis.

Select one:

a.

-10.14 to -6.60 ng/mL

b.

-13.36 to -6.52 ng/mL

c.

-11.52 to -7.76 ng/mL

d.

-12.73 to -8.27 ng/mL

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Question6

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Recall in our discussion of the binomial distribution the research study that examined schoolchildren developing nausea and vomiting following holiday parties. The intent of this study was to calculate probabilities corresponding to a specified number of children becoming sick out of a given sample size. Recall also that the probability, i.e. the binomial parameter "p" defined as the probability of "success" for any individual, of a randomly selected schoolchild becoming sick was given.

Suppose you are now in a different reality, in which this binomial probability parameterpis now unknown to you but you are still interested in carrying out the original study described above, though you must first estimatepwith a certain level of confidence. You obtain research funding to randomly sample 15 schoolchildren with an inclusion criterion that he/she must have recently attended a holiday party, and conduct a medical evaluation by a certified pediatrician. After anxiously awaiting your pediatrician colleague to complete her medical assessments, she emails you data contained in the following table.

SubjectNausea and

Vomiting?112130405060718190101110120131140150What is the estimated 95% confidence interval (CI) of the proportion of schoolchildren developing nausea and vomiting following holiday parties?

Please note the following: 1) 0 and 1 are defined as no and yes, respectively, which is a typical coding scheme in Public Health; 2) you might calculate a CI that is different from any of the multiple choice options listed below due to rounding differences, therefore select the closest match; and 3) you may copy and paste the data into Excel to facilitate analysis.

Select one:

a.

0.152 to 0.648

b.

0.141 to 0.606

c.

0.137 to 0.713

d.

0.169 to 0.752

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Question7

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Recall in our discussion of the normal distribution the research study that examined the blood vitamin D levels of the entire US population of landscape gardeners. The intent of this large-scale and comprehensive study was to characterize fully this population of landscapers as normally distributed with a corresponding population mean and standard deviation, which were determined from the data collection of the entire population.

Suppose you are now in a different reality in which this study never took place though you are still interested in studying the average vitamin D levels of US landscapers. In other words, the underlying population mean and standard deviation are now unknown to you. Furthermore, you would like to examine if wearing tank tops instead of short sleeve shirts significantly effects vitamin D levels. To accomplish this, you propose to collect data from the landscapers at two different points in time. Specifically, the landscapers are to wear short sleeve shirts while outside working during a period of three weeks. After three weeks, you collect blood specimens and the landscapers are then to wear tank tops for the next three weeks under the same working conditions, after which you collect blood draws a second time. You obtain research funding to randomly sample 18 landscapers, collect blood samples at two different time points as described above, and send these samples to your collaborating lab in order to quantify the amount of vitamin D in the landscapers' blood. After anxiously awaiting your colleagues to complete their lab quantification protocol, they email you the following vitamin D level data as shown in the following table.

SubjectTime Point 1, Shirts

Vitamin D (ng/mL)Time Point 2, Tank Tops

Vitamin D (ng/mL)144.26441.080258.89038.460341.80635.518461.74846.937559.52545.075644.20635.969747.70636.606846.55937.420956.55336.9821047.65038.4201154.18838.5981256.86834.9741358.40532.4561438.53440.2991554.86534.5491659.11033.3421748.36729.2521860.01339.737What is the estimated 95% confidence interval (CI) of the average difference in blood vitamin D levels between short sleeve shirt and tank top attire amongst US landscapers in ng/mL?

Please note the following: 1) in practice, you as the analyst decide how to calculate the difference in vitamin D levels between time points for a given study participant, and subsequently interpret the aggregated results appropriately in the context of the data, though for the purposes of this exercise the difference is assigned for you as follows.Define the difference as the second minus the first time points, which is common practice, since the plus or minus sign of the resulting difference reflects any change over sequential time; 2) you might calculate a CI that is different from any of the multiple choice options listed below due to rounding differences, therefore select the closest match; 3) ensure you use either the large or small sample CI formula as appropriate; and 4) you may copy and paste the data into Excel to facilitate analysis.

Select one:

a.

-18.51 to -10.77 ng/mL

b.

-21.48 to -11.96 ng/mL

c.

-15.74 to -9.16 ng/mL

d.

-21.38 to -9.64 ng/mL

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Question8

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Recall in our discussion of the normal distribution the research study that examined the blood vitamin D levels of the entire US population of landscape gardeners. The intent of this large-scale and comprehensive study was to characterize fully this population of landscapers as normally distributed with a corresponding population mean and standard deviation, which were determined from the data collection of the entire population.

Suppose you are now in a different reality in which this study never took place though you are still interested in studying the average vitamin D levels of US landscapers. In other words, the underlying population mean and standard deviation are now unknown to you. You obtain research funding to randomly sample 38 landscapers, collect blood samples, and send these samples to your collaborating lab in order to quantify the amount of vitamin D in the landscapers' blood. After anxiously awaiting your colleagues to complete their lab quantification protocol, they email you the following vitamin D level data as shown in the following table.

SubjectVitamin D134.844231.691341.013430.039542.248631.452737.699840.553940.5111035.4721142.4661236.4021333.0451427.8531537.5861632.7851743.0771832.9261937.7372038.1322131.8082242.2712342.3812438.7782543.1942640.2332738.2032841.7262940.2303031.9113138.4623246.7813345.9763436.0913529.3913636.0163743.0343846.539What is the estimated 95% confidence interval (CI) of the average blood vitamin D level of US landscapers in ng/mL?

Please note the following: 1) you might calculate a CI that is different from any of the multiple choice options listed below due to rounding differences, therefore select the closest match; 2) ensure you use either the large or small sample CI formula as appropriate; and 3) you may copy and paste the data into Excel to facilitate analysis.

Select one:

a.

30.9 to 35.5 ng/mL

b.

36.3 to 39.5 ng/mL

c.

33.6 to 42.5 ng/mL

d.

31.6 to 35.1 ng/mL

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Question9

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Recall in our discussion of the binomial distribution the research study that examined schoolchildren developing nausea and vomiting following holiday parties. The intent of this study was to calculate probabilities corresponding to a specified number of children becoming sick out of a given sample size. Recall also that the probability, i.e. the binomial parameter "p" defined as the probability of "success" for any individual, of a randomly selected schoolchild becoming sick was given.

Suppose you are now in a different reality, in which this binomial probability parameterpis now unknown to you but you are still interested in carrying out the original study described above, though you must first estimatepwith a certain level of confidence. You obtain research funding to randomly sample 42 schoolchildren with an inclusion criterion that he/she must have recently attended a holiday party, and conduct a medical evaluation by a certified pediatrician. After anxiously awaiting your pediatrician colleague to complete her medical assessments, she emails you data contained in the following table.

SubjectNausea and

Vomiting?102031415161718090101110120130140150160171181190200210220231240250260270280290301310320330340351360371380391401410420What is the estimated 95% confidence interval (CI) of the proportion of schoolchildren developing nausea and vomiting following holiday parties?

Please note the following: 1) 0 and 1 are defined as no and yes, respectively, which is a typical coding scheme in Public Health; 2) you might calculate a CI that is different from any of the multiple choice options listed below due to rounding differences, therefore select the closest match; and 3) you may copy and paste the data into Excel to facilitate analysis.

Select one:

a.

0.202 to 0.538

b.

0.172 to 0.547

c.

0.191 to 0.476

d.

0.161 to 0.512

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Question10

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Recall in our discussion of the binomial distribution the research study that examined schoolchildren developing nausea and vomiting following holiday parties. The intent of this study was to calculate probabilities corresponding to a specified number of children becoming sick out of a given sample size. Recall also that the probability, i.e. the binomial parameter "p" defined as the probability of "success" for any individual, of a randomly selected schoolchild becoming sick was given.

Suppose you are now in a different reality, in which this binomial probability parameterpis now unknown to you but you are still interested in carrying out the original study described above, though you must first estimatepwith a certain level of confidence. Furthermore, you would also like to collect data from adults to examine the difference between the proportion with nausea and vomiting following holiday parties of schoolchildren and adults, which will reflect any possible age differences in becoming sick. You obtain research funding to randomly sample 45 schoolchildren and 50 adults with an inclusion criterion that a given participant must have recently attended a holiday party, and conduct a medical evaluation by a certified pediatrician and general practitioner for the schoolchildren and adults, respectively. After anxiously awaiting your medical colleagues to complete their medical assessments, they email you data contained in the following tables.

Table 1. SchoolchildrenSubjectNausea and

Vomiting?102030405060708190100110120130140150161170180190200210221230240250260270280290300310321330340350360370380390401410420430440450Table 2. AdultsSubjectNausea and

Vomiting?102030405161718090100110120131140151160170180190200211221230240251260270280291301311320330340350360370380390400410420430441450460471480490500What is the estimated 95% confidence interval (CI) of the difference in proportions between schoolchildren and adults developing nausea and vomiting following holiday parties? Assign groups 1 and 2 to be schoolchildren and adults, respectively.

Please note the following: 1) in practice, you as the analyst decide how to assign groups 1 and 2 and subsequently interpret the results appropriately in the context of the data, though for the purposes of this exercise the groups are assigned for you; 2) 0 and 1 are defined as no and yes, respectively, which is a typical coding scheme in Public Health; 3) you might calculate a CI that is different from any of the multiple choice options listed below due to rounding differences, therefore select the closest match; and 4) you may copy and paste the data into Excel to facilitate analysis.

Select one:

a.

-0.3012 to 0.0035

b.

-0.2817 to 0.0038

c.

-0.2802 to 0.0039

d.

-0.3344 to 0.0040