Question 1081064: Hi, I've finished most of the questions already, but would like someone to check it they are correct. Thank you tutors for the help in advance!
We gather a sample of 100 people from a College and measure everyone’s age in the sample. The average age is 26 with a sample standard deviation of 3 years.
What is average of a student?
ans:26
Why does X ̅ vary randomly?
ans: different ages/dates equals different results(?)
What is our best guess of the distribution of X ̅?
ans: random(?)
Construct a 90% C.I.?
ans: 23.2, 28.8
Is it plausible that µ is 27 years old?
ans: yes
Test the hypothesis that u is greater than 27 years old a=.05?
ii.Is the hypothesis considered one sided or two sided?
one sided
iii.If the hypothesis is true, what is the distribution of X ̅ ?
random
iv.Is the answer to part (iii) the same as 2c?
yes
v.What is the value of the TTest?
.025
vii. What is TCritical?
2
viii.Is the hypothesis likely or not likely to be true?
true
ix.If your conclusion in part viii is wrong, what type of error did you make?
type II
x.In this example, what is the probability of a type 1 error?
.004
xi.Use the 68-96-99.7 rule to approximate the p-value. What is the approximate p-value?
.018
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! What is average of a student?
ans:26
Why does X ̅ vary randomly?
BECAUSE DIFFERENT SAMPLES WOULD HAVE DIFFERENT AVERAGES/MEANS
What is our best guess of the distribution of X ̅?
THE BEST GUESS OF THE MEAN IS 26 AND THE BEST GUESS OF THE SD IS 3, BECAUSE THIS IS THE ONLY INFORMATION WE HAVE.
Construct a 90% C.I.? NOTE: 1-SIDED CONFIDENCE INTERVALS ARE MORE DIFFICULT, SO HERE I WILL USE A TWO-SIDED ONE
ans: (25.5, 26.5)
Is it plausible that µ is 27 years old?
BECAUSE THE 90% CONFIDENCE INTERVAL FAILS TO CONTAIN THE VALUE 27, WE SAY THAT IT IS UNLIKELY TO BE 27.
Test the hypothesis that u is greater than 27 years old a=.05?
ii.Is the hypothesis considered one sided or two sided?
one sided
iii.If the hypothesis is true, what is the distribution of X ̅ ?
Ho: MU < =27
Ha: MU >27
THE SAMPLING DISTRIBUTION IS MEAN 26 AND SD 0.3 THE SD COMES FROM s/sqrt(n)=3/10
t(df=99,0.90). t >1.29 is critical value.
t=(26-27)/0.3=-3.33.
Fail to reject Ho.
iv.Is the answer to part (iii) the same as 2c?
yes and no. It is not likely to be 27 in both instances, and it is definitely not likely to be greater than 27 even with a one-way test
v.What is the value of the TTest?
IT IS (26-27)/0.3=-3.33
vii. What is Critical?t >1.29
2
viii.Is the hypothesis likely or not likely to be true?
THE NULL HYPOTHESIS IS LIKELY TO BE TRUE. I WOULD HAVE PHRASED THE QUESTION REGARDING THE NULL HYPOTHESIS. THE EXPERIMENTAL HYPOTHESIS IS NOT TRUE.
ix.If your conclusion in part viii is wrong, what type of error did you make?
TYPE II, BECAUSE IF WE ACCEPT A FALSE Ho, WE ARE MAKING AN ERROR OF THE SECOND TYPE.
x.In this example, what is the probability of a type 1 error? ACTUALLY 0. THE PROBLEM HERE IS THAT THE SAMPLE MEAN IS 26 AND WE ARE HYPOTHESIZING THAT THE TRUE VALUE IS GREATER THAN 27 WITH A SAMPLE SIZE OF 100, AND THAT IS IMPOSSIBLE BECAUSE THE CONFIDENCE INTERVAL WILL ALWAYS CONTAIN A VALUE LESS THAN 27. AM I MISREADING SOMETHING?
xi.Use the 68-96-99.7 rule to approximate the p-value. What is the approximate p-value? 1.
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