It has long been assumed that first year college students gain weight during their first semester. During the last year, some college students have lived on campus (OC) and some have gone to school remotely (RM). Do on campus students gain more weight than remote students? A random sample 77 OC students had a mean weight gain of x = 3.46 pounds. A random sample 93 RMs a mean weight of y = 2.35 pounds. It is recognized that the true standard deviation of OC weight gain is ?x = 3.16 pounds while it is recognized that the true standard deviation of RM weight gain is ?y = 2.07 pounds. The true (unknown) mean OC weight gain is ?x pounds, while the true (unknown) mean of RM weight gain is ?y pounds. Weights are known to be a normally distributed. In summary: It has long been assumed that first year college students gain weight during their first semester. During the last year, some college students have lived on campus (OC) and some have gone to school remotely (RM). Do oncampus students gain more weight than remote students? A random sample 77 OC students had a mean weight gain of x = 3.46 pounds. A random sample 93 RMs a mean weight of y = 2.35 pounds. It is recognized thatthe true standard deviation of OC weight gain is oy = 3.16 pounds while it is recognized that the true standard deviation of RM weight gain is oy = 2.07 pounds. The true (unknown) mean OC weight gain is lx pounds,while the true (unknown) mean of RM weight gain is µy pounds. Weights are known to be a normally distributed. In summary:ТуреOn campus data(OC) 77Remote data (RM)) 93Sample Size Sample Mean Standard Deviation3.162.073.462.35a)Calculate the variance of the random variable X which is the mean of the weights of the 77 AMs from 2019. 0.1297b)Calculate the variance of the random variable Y, which is the mean of the weights of the 93 AMs from 1999. 0.0461c) Calculate the variance of X - Y? 0.1758d) Calculate the standard deviation of X - Y? 0.4193e) If we wish to create an 98% confidence interval for Uy - Hy then what is the z critical value used? 2.363f)Create an 98% confidence interval for Hx - Hy. (0.13462.0853g) What is the length of your 98% confidence interval for Hx - Hy ? 1.9507h) If we used this data to test Họ: Hx - Hy =0 against the alternative H3: u, - Hy > 0 then what would the value of the calculated test statistic z have been? 2.6473i) If we used this data to test Họ: Hx - Hy =0 against the alternative H3: µx - Hy >0 then what would the p value have been? 0.0041j)If we used this data to test Ho: Hx - Hy =0 against the alternative H3: Hx - Hy #0 then what would the p value have been? 0.0081|k) Copy your R script for the above into the text box here.

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It has long been assumed that first year college students gain weight during their first semester. During the last year, some college students have lived on campus (OC) and some have gone to school remotely (RM). Do on campus students gain more weight than remote students? A random sample 77 OC students had a mean weight gain of x = 3.46 pounds. A random sample 93 RMs a mean weight of y = 2.35 pounds. It is recognized that the true standard deviation of OC weight gain is

?_x

= 3.16 pounds while it is recognized that the true standard deviation of RM weight gain is

?_y

= 2.07 pounds. The true (unknown) mean OC weight gain is

?_x

pounds, while the true (unknown) mean of RM weight gain is

?_y

pounds. Weights are known to be a normally distributed. In summary:

It has long been assumed that first year college students gain weight during their first semester. During the last year, some college students have lived on campus (OC) and some have gone to school remotely (RM). Do on
campus students gain more weight than remote students? A random sample 77 OC students had a mean weight gain of x = 3.46 pounds. A random sample 93 RMs a mean weight of y = 2.35 pounds. It is recognized that
the true standard deviation of OC weight gain is oy = 3.16 pounds while it is recognized that the true standard deviation of RM weight gain is oy = 2.07 pounds. The true (unknown) mean OC weight gain is lx pounds,
while the true (unknown) mean of RM weight gain is µy pounds. Weights are known to be a normally distributed. In summary:
Туре
On campus data(OC) 77
Remote data (RM)) 93
Sample Size Sample Mean Standard Deviation
3.16
2.07
3.46
2.35
a)Calculate the variance of the random variable X which is the mean of the weights of the 77 AMs from 2019. 0.1297
b)Calculate the variance of the random variable Y, which is the mean of the weights of the 93 AMs from 1999. 0.0461
c) Calculate the variance of X - Y? 0.1758
d) Calculate the standard deviation of X - Y? 0.4193
e) If we wish to create an 98% confidence interval for Uy - Hy then what is the z critical value used? 2.363
f)Create an 98% confidence interval for Hx - Hy. (0.1346
2.0853
g) What is the length of your 98% confidence interval for Hx - Hy ? 1.9507
h) If we used this data to test Họ: Hx - Hy =0 against the alternative H3: u, - Hy > 0 then what would the value of the calculated test statistic z have been? 2.6473
i) If we used this data to test Họ: Hx - Hy =0 against the alternative H3: µx - Hy >0 then what would the p value have been? 0.0041
j)If we used this data to test Ho: Hx - Hy =0 against the alternative H3: Hx - Hy #0 then what would the p value have been? 0.0081|
k) Copy your R script for the above into the text box here.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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