Hint: For this problem pay attention to how you determine when a question is ask

Question

Hint: For this problem pay attention to how you determine when a question is asking about the difference between proportions and when it is asking about the difference between means.

2.) Given below are samples of enrollment from medical schools that specialize in research and from those that specialize in primary care. You need to decide if there is a difference in the average enrollment for the two specializations.

Research 474 577 605 663 783 467 670 414 813 443 565 696 692 694 277 419 884

Primary Care 783 605 427 728 546 474 371 107 442 587 293 277 662 555 527 320

a. (0.25 point) Find the 95% confidence interval for the difference between the means and interpret the interval in the context of the problem. b. (0.25 point) Write the two hypotheses for this problem.

c. (0.25 point) Find the test-statistic (i.e. t) and p-value. Sketch the distribution of test-statistics and indicate t and the shaded region corresponding to the p-value.

d. (0.25 point) In the context of the problem, make a conclusion and substantiate with statistical arguments.

Explanation / Answer

a.
CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x1)=596.2353
Standard deviation( sd1 )=163.2362
Sample Size(n1)=17
Mean(x2)=481.5
Standard deviation( sd2 )=179.3957
Sample Size(n2)=16
CI = [ ( 596.2353-481.5) ±t a/2 * Sqrt( 26646.05699044/17+32182.81717849/16)]
= [ (114.7353) ± t a/2 * Sqrt( 3578.8412) ]
= [ (114.7353) ± 2.131 * Sqrt( 3578.8412) ]
= [-12.7484 , 242.219]

b.
Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate Hypothesis, There Is Significance between them - H1: u1 != u2
c.
Test Statistic
X(Mean)=596.2353
Standard Deviation(s.d1)=163.2362 ; Number(n1)=17
Y(Mean)=481.5
Standard Deviation(s.d2)=179.3957; Number(n2)=16
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =596.2353-481.5/Sqrt((26646.05699/17)+(32182.81718/16))
to =1.918
| to | =1.918

d.
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 1.9179 ) = 0.074
Hence Value of P0.05 < 0.074,Here We Do not Reject Ho

Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 15 d.f is 2.131
We got |to| = 1.9179 & | t | = 2.131
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho

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