a)Calculate the variance of the random variable X which is the mean of the weights of the 77 AMs from 2019. b)Calculate the variance of the random variable Y, which is the mean of the weights of the 93 AMs from 1999. c) Calculate the variance of X - Y?
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
= 3.16 pounds while it is recognized that the true standard deviation of RM weight gain is
= 2.07 pounds. The true (unknown) mean OC weight gain is
pounds, while the true (unknown) mean of RM weight gain is
pounds. Weights are known to be a
| Type | Sample Size | Sample Mean | Standard Deviation |
|---|---|---|---|
| On campus data(OC) | 77 | 3.46 | 3.16 |
| Remote data (RM)) | 93 | 2.35 | 2.07 |
a)Calculate the variance of the random variable X which is the mean of the weights of the 77 AMs from 2019.
b)Calculate the variance of the random variable Y, which is the mean of the weights of the 93 AMs from 1999.
c) Calculate the variance of X - Y?
d) Calculate the standard deviation of X - Y?
.
e) If we wish to create an 98% confidence interval for
-
then what is the z critical value used?
f)Create an 98% confidence interval for
-
. (
)
g) What is the length of your 98% confidence interval for
-
?
h) If we used this data to test
-
=0 against the alternative
-
> 0 then what would the value of the calculated test statistic z have been?
i) If we used this data to test
-
=0 against the alternative
-
>0 then what would the p value have been?
j)If we used this data to test
-
=0 against the alternative
-
≠0 then what would the p value have been?
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