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N76 [4]
3 years ago
6

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.

Mathematics
1 answer:
mina [271]3 years ago
3 0

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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Step-by-step explanation:

The question is incomplete. Here is the complete question.

A student has 10 coins in her pocket that have a value of $0.85. The coins are either nickels or dimes. If each nickel costs $0.05 and each dime costs $0.10. Which system of linear equations represents this scenario?

Let the number of nickel in the pocket of the student be p

Let the number of dime in the pocket of the student be q

If there are 10 coins in her pocket, then the total coins in her pocket will be represented by the equation;

p+q = 10...... 1

If each nickel costs $0.05, p nickels will cost $0.05×p = $0.05p

If each dime costs $0.10, q nickel will costs $0.10×q = $0.10q

Total amount will be $0.05p+$0.10q

Now if the total coins in her pocket has a value of $0.85, then the we will equate $0.05p+$0.10q to $0.85 to give our second linear equation as:

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Therefore, the system of linear equations represents this scenario are:

p+q = 10...... 1

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Step-by-step explanation:

If you create a mini graph, like I did, you would have seen that the middle point is at the co-ordinates (3,6). I have attached a image to this reply, with my "graph". (Sorry if its a little ugly, but that doesn't matter, the math does.)

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