CA random sample of 16 participants is selected from a population with a mean de

Question

CA random sample of 16 participants is selected from a population with a mean depression score of mu = 20. After a treatment is administered to the individuals in the sample, the sample mean of the depression score is found to be X = 18 and the sample standard deviation s - 5. Can we conclude that the treatment has a significant effect on depression? Which hypothesis test you should use. z-test or t-test? Do the test. Step 1: Stale the hypotheses both in words and in symbols. H0: H1: Step 2: alpha =.05. What are the critical values? Step 3: Calculate test statistics. Step 4: Make a decision. Step 5: State a conclusion.

Explanation / Answer

t-test For Single Mean
Set Up Hypothesis
Null, H0: U=20
Alternate, H1: U!=20
Test Statistic
Population Mean(U)=20
Sample X(Mean)=18
Standard Deviation(S.D)=5
Number (n)=16
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =18-20/(5/Sqrt(16))
to =-1.6
| to | =1.6
Critical Value
The Value of |t | with n-1 = 15 d.f is 2.131
We got |to| =1.6 & | t | =2.131
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -1.6 ) = 0.1304
Hence Value of P0.05 < 0.1304,Here We Do not Reject Ho

[ANSWERS]
1. T-test
2. H0: U=20 , H1: U!=20
3. -2.131,+2.131
4. to =-1.6
5. Do not Reject Ho
6. There is no significance effect with the treatment after result

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