To test the effectiveness of a treatment, a sample is selected from a normal pop
ID: 3133082 • Letter: T
Question
To test the effectiveness of a treatment, a sample is selected from a normal population with a mean of = 40 and a standard deviation of = 12. After the treatment is administered to the individuals in the sample, the sample mean is found to be M = 46.
(a) If the sample consists of n = 4 individuals, is this result sufficient to conclude that there is a significant treatment effect? Use a two-tailed test with = .05. (Use 2 decimal places.)
-critical = ±
z=
Conclusion
Reject the null hypothesis, there is a significant treatment effect.
Reject the null hypothesis, there is not a significant treatment effect.
Fail to reject the null hypothesis, there is not a significant treatment effect.
Fail to reject the null hypothesis, there is a significant treatment effect.
If the sample consists of n = 36 individuals, is this result sufficient to conclude that there is a significant treatment effect? Use a two-tailed test with = .05. (Use 2 decimal places.)
-critical = ±
z=
Conclusion
Fail to reject the null hypothesis, there is a significant treatment effect.
Reject the null hypothesis, there is not a significant treatment effect.
Fail to reject the null hypothesis, there is not a significant treatment effect.
Reject the null hypothesis, there is a significant treatment effect.
(c) Compute Cohen's d to measure effect size for both tests (n = 4 and n = 36). (Use 2 decimal places.)
n = 4
n = 36
(d) Briefly describe how sample size influences the outcome of the hypothesis test. How does sample size influence measures of effect size?
A larger sample increases the likelihood of rejecting the null hypothesis, but has no influence on Cohen's d.
A larger sample increases the likelihood of rejecting the null hypothesis, but has a decreasing effect on Cohen's d.
A larger sample increases the likelihood of rejecting the null hypothesis and increases Cohen's d.
A larger sample reduces the likelihood of rejecting the null hypothesis, but has no influence on Cohen's d.
Explanation / Answer
Testing of hypothesis and Cohen’s d
To test the effectiveness of a treatment, a sample is selected from a normal population with a mean of = 40 and a standard deviation of = 12. After the treatment is administered to the individuals in the sample, the sample mean is found to be M = 46.
(a) If the sample consists of n = 4 individuals, is this result sufficient to conclude that there is a significant treatment effect? Use a two-tailed test with = .05. (Use 2 decimal places.)
-critical = ±
z=1.96
Z Test of Hypothesis for the Mean
Data
Null Hypothesis m=
40
Level of Significance
0.05
Population Standard Deviation
12
Sample Size
4
Sample Mean
46
Intermediate Calculations
Standard Error of the Mean
6.0000
Z Test Statistic
1.0000
Two-Tail Test
Lower Critical Value
-1.9600
Upper Critical Value
1.9600
p-Value
0.3173
Do not reject the null hypothesis
Conclusion
Reject the null hypothesis, there is a significant treatment effect.
Reject the null hypothesis, there is not a significant treatment effect.
Fail to reject the null hypothesis, there is not a significant treatment effect.
Fail to reject the null hypothesis, there is a significant treatment effect.
Correct Answer: Fail to reject the null hypothesis, there is not a significant treatment effect.
If the sample consists of n = 36 individuals, is this result sufficient to conclude that there is a significant treatment effect? Use a two-tailed test with = .05. (Use 2 decimal places.)
-critical = ±
z=1.96
Z Test of Hypothesis for the Mean
Data
Null Hypothesis m=
40
Level of Significance
0.05
Population Standard Deviation
12
Sample Size
36
Sample Mean
46
Intermediate Calculations
Standard Error of the Mean
2.0000
Z Test Statistic
3.0000
Two-Tail Test
Lower Critical Value
-1.9600
Upper Critical Value
1.9600
p-Value
0.0027
Reject the null hypothesis
Conclusion
Fail to reject the null hypothesis, there is a significant treatment effect.
Reject the null hypothesis, there is not a significant treatment effect.
Fail to reject the null hypothesis, there is not a significant treatment effect.
Reject the null hypothesis, there is a significant treatment effect.
Correct Answer: Reject the null hypothesis, there is not a significant treatment effect.
(c) Compute Cohen's d to measure effect size for both tests (n = 4 and n = 36). (Use 2 decimal places.)
n = 4
Cohen’s d = (46 – 40) / 6 = 1.00
n = 36
Cohen’s d = (46 – 40) / 2 = 3.00
(d) Briefly describe how sample size influences the outcome of the hypothesis test. How does sample size influence measures of effect size?
A larger sample increases the likelihood of rejecting the null hypothesis, but has no influence on Cohen's d.
A larger sample increases the likelihood of rejecting the null hypothesis, but has a decreasing effect on Cohen's d.
A larger sample increases the likelihood of rejecting the null hypothesis and increases Cohen's d.
A larger sample reduces the likelihood of rejecting the null hypothesis, but has no influence on Cohen's d.
Correct Answer: A larger sample increases the likelihood of rejecting the null hypothesis, but has a decreasing effect on Cohen's d.
Z Test of Hypothesis for the Mean
Data
Null Hypothesis m=
40
Level of Significance
0.05
Population Standard Deviation
12
Sample Size
4
Sample Mean
46
Intermediate Calculations
Standard Error of the Mean
6.0000
Z Test Statistic
1.0000
Two-Tail Test
Lower Critical Value
-1.9600
Upper Critical Value
1.9600
p-Value
0.3173
Do not reject the null hypothesis
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