Reference no: EM132377594
Assignment
1. A consumer group is collecting data on the mean cost (in dollars) of a shoulder MRI across different state imaging facilities. They use the following SAS program and output to analyze their data.
data; input cost @@; datalines;
1200 800 700 440 1100 4500 3000 600 4000 750
;
procttesth0=1000 sides=u alpha=0.05;
procttesth0=1000 sides=l alpha=0.05;
procttesth0=1000 sides=2alpha=0.05;
run;
a) Test whether the mean cost is equal to $1000. What is the p-value?
b) Construct the 95% Confidence Interval for the mean cost. Then calculate the 99% (Yes 99%) Confidence Interval for the mean cost.
c) Now test the null hypothesis that the mean cost is less than or equal to 1000 versus the alternative hypothesis that the mean cost is greater than 1000. What is the p-value?
d)
2. The admission committee was wondering whether the average GRE scores had increased over time. To examine this question they looked at data from students applying in two different years, 2000 and 2019.
|
2000
|
2019
|
|
500
|
560
|
|
450
|
460
|
|
600
|
620
|
|
700
|
720
|
|
550
|
540
|
|
551
|
600
|
|
552
|
750
|
a) Does the assumption that the samples come from two normal populations seem reasonable here? Why? Is the assumption that the two population variances are equal here correct? Why?
b) What is the mean score (with 95% Confidence) for students in 2000? What about for 2019?
c) Formally test whether the mean score differs for the two years at alpha=0.05.
3. A Yale student wishes to invest some money in a new cosmetics company. The CEO of the cosmetics company says that they have a new product that makes users look years younger after using it. The Yale student is intrigued but asks for some data to support this claim.
The CEO provides data for 5 persons before and after using the product. The data gives the age that the user felt they looked before and after the product use. The Yale student took this data and ran the following SAS program. The output for this program is also listed.
dataskincream; input before after;
agelook=before-after;
cards;
76 23
75 44
88 56
56 29
66 20
run;
procmeansmeanstdstderrtprtclm; run;
The MEANS Procedure
Lower 95% Upper 95%
Variable Mean Std Dev Std Error t Value Pr> |t| CL for Mean CL for Mean
???????????????????????????????????????????
before 72.2000000 11.9666202 5.3516353 13.49 0.0002 57.3414785 87.0585215
after 34.4000000 15.2085502 6.8014704 5.06 0.0072 15.5160907 53.2839093
agelook 37.8000000 11.1220502 4.9739320 7.60 0.0016 23.9901507 51.6098493
???????????????????????????????????????????
a) Do the data suggest that the cosmetic makes any difference in how old the user felt s/he looked? Use alpha = 0.05.
b) Now test the CEO’s specific claim that the cosmetic is associated with a 10 year reduction in perceived age.
4. A group of 12 friends tried three diets (1=Keto, 2=Weight Watchers, 3=South Beach) in an effort to get ready for the summer. Each friend tried each diet for one month and lost weight (in pounds) as below.
a) What is the overall variance in weight loss? How much of this variance is explained by the full model?
b) Fill in the statistical formulas for the table below
|
Analysis of Variance
|
|
Source
|
DF
|
Sum of
Squares
|
|
Model
|
|
|
|
Error
|
|
|
|
Corrected Total
|
|
|
c) Is there any difference among the three diets in terms of weight loss?
d) If the variable FRIEND was not included in the analysis would your answer to part c be the same?
e) Which diet is the best in terms of weight loss?
Attachment:- SAS program.rar