The following is data about the hemoglobin concentrations of volunteers collected at sea level and at an altitude of 11000 feet. sea level concentrations = [14.70 , 15.22, 15.28, 16.58, 15.10 , 15.66, 15.91, 14.41, 14.73, 15.09, 15.62, 14.92] 11000 feet concentrations = [14.81, 15.68, 15.57, 16.59, 15.21, 15.69, 16.16, 14.68, 15.09, 15.30 , 16.15, 14.76] There are two alternative scenarios about the way the data were obtained. In scenario 1, there are 12 volunteers who lived for a month at sea level, at which time blood was drawn and the data in "sea level concentrations" dataset were obtained. Subsequently, all 12 volunteers were moved to 11000 ft and after a month the data in the "11000 feet concentrations" dataset obtained. There is a one to one correspondence between the numbers in the two datasets, that is the first numbers correspond to volunteer1, the second numbers to volunteer2 etc. In scenario 2, the "sea level concentrations" dataset is a random sample obtained from 12 people living at sea level and the "11000 feet concentrations" dataset is a random sample obtained from 12 different people living at 11000 feet. In this case there is no correlation between the individual numbers in the two datasets. For each of these scenarios, calculate the standard errors of the mean differences or difference between of the means of the samples as well as the corresponding 95% confidence intervals. Perform the appropriate t-test for each scenario. Assume equal variances between the samples and two-tailed hypotheses. Round off all answers to two digits after the decimal point. Since the sign of the t-statistic depends on the arbitrary choice of which data to subtract from which and to simplify grading, wherever applicable report the absolute value of the t-statistic. 1) In scenario 2, what is the width (upper bound - lower bound) of the 95% confidence interval for the difference of the mean hemoglobin concentrations between the two samples? Input the absolute value (if you get a negative number input - that number)
The following is data about the hemoglobin concentrations of volunteers collected at sea level and at an altitude of 11000 feet.
sea level concentrations =
[14.70 , 15.22, 15.28, 16.58, 15.10 , 15.66, 15.91, 14.41, 14.73, 15.09, 15.62, 14.92]
11000 feet concentrations = [14.81, 15.68, 15.57, 16.59, 15.21, 15.69, 16.16, 14.68, 15.09, 15.30 , 16.15, 14.76]
There are two alternative scenarios about the way the data were obtained.
In scenario 1, there are 12 volunteers who lived for a month at sea level, at which time blood was drawn and the data in "sea level concentrations" dataset were obtained. Subsequently, all 12 volunteers were moved to 11000 ft and after a month the data in the "11000 feet concentrations" dataset obtained. There is a one to one correspondence between the numbers in the two datasets, that is the first numbers correspond to volunteer1, the second numbers to volunteer2 etc.
In scenario 2, the "sea level concentrations" dataset is a random sample obtained from 12 people living at sea level and the
"11000 feet concentrations" dataset is a random sample obtained from 12 different people living at 11000 feet. In this case there is no
For each of these scenarios, calculate the standard errors of the mean differences or difference between of the means of the samples as well as the corresponding 95% confidence intervals. Perform the appropriate t-test for each scenario. Assume equal variances between the samples and two-tailed hypotheses.
Round off all answers to two digits after the decimal point. Since the sign of the t-statistic depends on the arbitrary choice of which data to subtract from which and to simplify grading, wherever applicable report the absolute value of the t-statistic.
1)
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In scenario 2, what is the width (upper bound - lower bound) of the 95% confidence interval for the difference of the mean hemoglobin concentrations between the two samples? Input the absolute value (if you get a negative number input - that number). |
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