Ubing & Power or R: 2. A researcher investigates the effects of an after-school
ID: 3306409 • Letter: U
Question
Ubing & Power or R: 2. A researcher investigates the effects of an after-school program on elementary school students' self-esteem levels. A random sample of n-25 students is selected to participate in the program. Their mean self-esteem level after the program's completion is M = 84 (0-100 scale) with standard deviation of s = 15, The researcher compares her results to the general population of elementary school students who have a mean of -80. She wants to test the effect of this program using two-tailed t test with = .05 (a) What is the probability to find the significant result when there is no effect of the program? (b) What is the probability to fail to find the significant result when there is no effect of the program? (c) What is the probability to find the significant result when there is an effect of the program? (d) What is the probability to fail to find the significant result when there is an effect of the program? (e) What is the critical t value to reject the null hypothesis? (f) The research recruited 11 more participants and got the same sample mean and standard deviation. How does this change the answers to questions a - e?Explanation / Answer
> #Given
> Mean= 84
> mu=80
> s=15
> n=25
> Test_statistics = (Mean - mu)/(s/sqrt(n))
> Test_statistics
[1] 1.333333
>
a)
> P_value=2*pt(-abs(Test_statistics),df=n-1)
> P_value
[1] 0.1949407
b)
1 -0.194907 = 0.805093
e)
> qt(c(.025, .975), df=5)
[1] -2.570582 2.570582
This is the critical values using critical value we say that we fail to reject Ho,
f) No
> Mean= 84
> mu=80
> s=15
> n=25+11
> Test_statistics = (Mean - mu)/(s/sqrt(n))
> Test_statistics
[1] 1.6
> P_value=2*pt(-abs(Test_statistics),df=n-1)
>
> P_value
[1] 0.1185878
>
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