Psy 210 Practice Quiz 3 Answers
1. 2
2. z-score cut off for top 10% is 1.28
Convert this to GPA: GPA = z*new sd + new mean = 1.28*.5+2.75 = 3.39
3. z = 1.645 (1.64 and 1.65 are both the same distance from the desired proportion of .05, and so we
average them).
Score = z * 2 + 6 = 1.645 * 2 + 6 = 9.29
4. mu and sigma with a subscript for X-bar (written properly)
5. mean is 12
standard deviation = sigma / sqrt(n) = 3 / sqrt (30) = 3 / 5.4772 = .5477
6. A statistic is considered to be relatively efficient if it has a smaller standard error than
another statistic that could be used to estimate the same population parameter for a fixed
sample size.
7. The Central Limit Theorem states that as sample size increases, the _sampling_ distribution
of the mean approaches the _normal_ distribution with mean mu and standard deviation
_sigma/sqrt(n)_.
8.
a. Write the null hypothesis (1 mark)
H0: mu = 100, written properly
b. Draw the sampling distribution of the mean (2 marks)
X-axis should be labeled mean, X-bar, or mean MSCEIT
Y-axis should be labeled p
Mean should be 100
Standard deviation should be 15 / sqrt(25) = 15 / 5 = 3
Shape should be roughly normal
103 should be labeled and should be above 100
The area to the right of 103 should be shaded
c. Calculate the z-score (1 mark)
z = (x-bar – mu) / standard error = (103 – 100) / 3 = 1
d. Draw the standard normal distribution (1 mark)
X axis should be labeled z
Y axis should be labeled p
Mean should be 0
Standard deviation should be 1
Shape should be roughly normal
1 should be labeled and should be at about 1 standard deviation above the mean
area to the right of 1 should be shaded
e. Find the p-value (1 mark)
p = .1587
f. State if you retain or reject the null hypothesis. (1 mark)
Retain
