A dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population of cows. She randomly as
signs nold = 8 to get the old diet, and nnew = 5 to get the new diet including the additive. The cows are housed in 13 separated pens and each gets separate feed, with or without additive as appropriate. After two weeks, she picks a day and milks each cow using standard procedures and records the milk produced in pounds. The data are below:
Old Diet: 43, 51, 44, 47, 38, 46, 40, 35
New Diet: 47, 75, 85, 100, 58
Let µnew and µold be the population mean milk productions for the new and old diets, respectively. She wishes to test: H0 : µnew ? µold = 0 vs. HA : µnew ? µold 6= 0, using ? = 0.05.
(a) Are the two populations paired or independent? Explain your answer.
(b) Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you?
(c) Choose a test appropriate for the hypotheses above, and justify your choice based on your answers to parts (a) and (b). Then perform the test by computing a p-value, and making a reject or not reject decision. Do not use R for this, and show your work. Finally, state your conclusion in the context of the problem.
Old Diet: 43, 51, 44, 47, 38, 46, 40, 35
New Diet: 47, 75, 85, 100, 58
Let µnew and µold be the population mean milk productions for the new and old diets, respectively. She wishes to test: H0 : µnew ? µold = 0 vs. HA : µnew ? µold 6= 0, using ? = 0.05.
(a) Are the two populations paired or independent? Explain your answer.
(b) Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you?
(c) Choose a test appropriate for the hypotheses above, and justify your choice based on your answers to parts (a) and (b). Then perform the test by computing a p-value, and making a reject or not reject decision. Do not use R for this, and show your work. Finally, state your conclusion in the context of the problem.
1 answer:
Answer:
Step-by-step explanation:
Given that a dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population of cows. She randomly assigns nold = 8 to get the old diet, and nnew = 5 to get the new diet including the additive.
From the data given we get the following
N Mean StDev SE Mean
Sample 1 8 43 5.1824 1.832
Sample 2 5 73 21.0832 9.429
df = 11
Std dev for difference = 13.3689
a) Yes the two are independent. The two sets of cows randomly chosen are definitely independent. Paired means equal number should be there and homogeneous conditions should be maintained.
b) Enclosed
c) Comparison of two means is the test recommended here. Because independent samples are used.\
d) Test statistic= -3.1233
(because of unequal variances we use that method)
95% confidence interval = ( -56.6676 , -3.3324 )
p value <0.05 our alpha
So reject null hypothesis.
The two means are statistically significantly different.
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Answer:
a) As we can see on the equation given the slope os 1.033 since is the value next to the city mpg (independent variable)
And on this case since the value for the slope is positive the best interpretation is:
E. On the average, highway mileage increases by 1.033 mpg for each additional mpg in city mileage
Because we see the if we increase on 1 unit the city mpg then the highway mpg would increase 1.033
b) For this case as we can see in the model the free term correspond to 6.785 and that correspond to the intercept for this case.
And the best interpretation is given by:
B. Because this is the highway mileage for zero city mpg.
For this reason is not meaningful since we are not interested on 0 or negative city mpg.
c) highway mpg = 6.785 + (1.033 × 18)=25.38 mpg
highway mpg = 6.785 + (1.033 × 25)=32.61 mpg
d) See the figure attached.
Step-by-step explanation:
For this case we have the following linear model:
highway mpg = 6.785 + (1.033 × city mpg)
(a) What is the slope of this line? Say in words what the numerical value of the slope tells us.
As we can see on the equation given the slope os 1.033 since is the value next to the city mpg (independent variable)
And on this case since the value for the slope is positive the best interpretation is:
E. On the average, highway mileage increases by 1.033 mpg for each additional mpg in city mileage
Because we see the if we increase on 1 unit the city mpg then the highway mpg would increase 1.033
(b) What is the intercept? (Enter your answer to three decimal places.)mpgExplain why the value of the intercept is not statistically meaningful.
For this case as we can see in the model the free term correspond to 6.785 and that correspond to the intercept for this case.
And the best interpretation is given by:
B. Because this is the highway mileage for zero city mpg.
For this reason is not meaningful since we are not interested on 0 or negative city mpg.
(c) Find the predicted highway mileage for a car that gets 18 miles per gallon in the city. (Round your answer to two decimal places.)______ mpgFind the predicted highway mileage for a car that gets 25 miles per gallon in the city. (Round your answer to two decimal places.)______ mpg
For this case we just need to replace into the formula and we got:
highway mpg = 6.785 + (1.033 × 18)=25.38 mpg
highway mpg = 6.785 + (1.033 × 25)=32.61 mpg
(d) Draw a graph of the regression line for city mileages between 10 and 50 mpg. (Be sure to show the scales for the x and y axes.)
See the figure attached
