Under some circumstances a 6-point treatment effect can be very large, and in so
ID: 3133077 • Letter: U
Question
Under some circumstances a 6-point treatment effect can be very large, and in some circumstances it can be very small. Assume that a sample of n = 25 individuals is selected from a population with a mean of = 70. A treatment is administered to the sample and, after treatment, the sample mean is found to be M = 76. Notice that the treatment appears to have increased scores by an average of 6 points.
(a) If the population standard deviation is = 19, is the 6-point effect large enough to be statistically significant? Use a two-tailed test with = 0.05. (Round your answers to two decimal places.)
z-critical =
± z =
Conclusion (chose A, B, C, D)
A) Reject the null hypothesis. There is not a significant treatment effect.
B) Fail to reject the null hypothesis. There is not a significant treatment effect.
C) Reject the null hypothesis. There is a significant treatment effect.
D) Fail to reject the null hypothesis. There is a significant treatment effect.
(b) If the population standard deviation is = 5, is the 6-point effect large enough to be statistically significant? Use a two-tailed test with = 0.05. (Round your answer to two decimal places.)
z-critical =
± z =
Conclusion (chose A, B, C, D)
A) Fail to reject the null hypothesis. There is a significant treatment effect.
B) Fail to reject the null hypothesis. There is not a significant treatment effect.
C) Reject the null hypothesis. There is not a significant treatment effect.
D) Reject the null hypothesis. There is a significant treatment effect.
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u = 70
Ha: u =/ 70
As we can see, this is a two tailed test.
Thus, getting the critical z, as alpha = 0.05 ,
alpha/2 = 0.025
zcrit = +/- 1.96 [ANSWER]
***************************************
Getting the test statistic, as
X = sample mean = 76
uo = hypothesized mean = 70
n = sample size = 25
s = standard deviation = 19
Thus, z = (X - uo) * sqrt(n) / s = 1.578947368 = 1.58 [ANSWER]
****************************************
As |z| < 1.96, we fail to reject Ho.
Hence,
OPTION B) Fail to reject the null hypothesis. There is not a significant treatment effect. [ANSWER]
*****************************************
B)
Formulating the null and alternative hypotheses,
Ho: u = 70
Ha: u =/ 70
As we can see, this is a two tailed test.
Thus, getting the critical z, as alpha = 0.05 ,
alpha/2 = 0.025
zcrit = +/- 1.96 [ANSWER]
****************************************
Getting the test statistic, as
X = sample mean = 76
uo = hypothesized mean = 70
n = sample size = 25
s = standard deviation = 5
Thus, z = (X - uo) * sqrt(n) / s = 6 [ANSWER]
**************************************
As |z| > 1.96, we reject Ho. Hence,
OPTION D) Reject the null hypothesis. There is a significant treatment effect. [ANSWER]
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