Download 2. A sample of n = 16 scores has a mean of M = 83 and a standard

2. A sample of n = 16 scores has a mean of M = 83 and a standard deviation of s = 12. A. Explain what is measured
by the sample standard deviation. b. Compute the estimated standard error for the sample mean and explain what is
measured by the standard error.
a) Sample standard deviation is the SD of the sample of 16 scores that has been drawn from the population.
In this case, it is 12.
(b) SE = s/√n = 12/√16 = 3
This is the standard deviation of the sampling distribution of the sample means. Thus, it is the standard deviation of the
distribution of the sample mean over repeated samples.
8. The following sample was obtained from a population with unknown parameters. Scores: 6, 12, 0, 3, 4 a. Compute
the sample mean and standard deviation. (Note that these are descriptive values that summarize the sample data). b.
Compute the estimated standard error for M. (Note that this is an inferential value that describes how accurately the
sample mean represents the unknown population mean).
(a)
Raw Scores:
x
d = x - x-bar
d^2
6
1
1
12
7
49
0
-5
25
3
-2
4
4
-1
1
Count =
5
Sums =
25
Mean, x-bar = Sum(x)/Count =
5
Variance, s^2 (Sample) = Sum(d^2)/(Count - 1) =
20.00
SD, s (Sample) = √(Sample variance) =
4.47
80
10. To evaluate the effect of a treatment, a sample of n = 9 individuals is obtained from a population with a mean of u
= 40, and a treatment is administered to the individuals in the sample. After treatment, the sample mean is found to
be M = 33. a. If the sample standard deviation is s = 9, are the data sufficient to conclude that the treatment has a
significant effect using a two-tailed test with x = .05? b. If the sample standard deviation is s= 15, are the data
sufficient to conclude that the treatment has a significant effect using a two-tailed test with x = .05?
(a)
Data:
n=9
μ = 40
s=9
x-bar = 33
(1) Formulate the hypotheses:
Ho: μ = 40
Ha: μ ≠ 40
(2) Decide the test statistic and the level of significance:
t (Two-tailed), α = 0.05
Degrees of freedom = 8
Lower Critical t- score = -2.3060
Upper Critical t- score = 2.3060
(3) State the decision Rule:
Reject Ho if |t| > 2.3060
(4) Calculate the value of test statistic:
SE = s/√n = 3.0000
t = (x-bar - μ)/SE = -2.3333
(5) Compare with the critical value and make a decision:
Since 2.3333 > 2.3060 we reject Ho and accept Ha
Decision: It appears that the mean is different from 40. The effect of the treatment is significant
(b)
Data:
n=9
μ = 40
s=9
x-bar = 33
(1) Formulate the hypotheses:
Ho: μ = 40
Ha: μ ≠ 40
(2) Decide the test statistic and the level of significance:
t(Two-tailed), α = 0.05
Degrees of freedom = 8
Lower Critical t- score = -2.3060
Upper Critical t- score = 2.3060
(3) State the decision Rule:
Reject Ho if |t| > 2.3060
(4) Calculate the value of test statistic:
SE = s/√n = 5.0000
t = (x-bar - μ)/SE = -1.40
(5) Compare with the critical value and make a decision:
Since 1.40 < 2.3060 we fail to reject Ho
Decision: There is no sufficient evidence that the mean is different from 40. The effect of the treatment is not
significant.