Chapter 5
Interpret a z-score of:
-1.75
1.75
The data point/ the score is 1.75 standard deviations below the mean.
The data point/ the score is 1.75 standard deviations above the mean.
What proportion of a normal distribution is located in the tail beyond a z-score of z = –1.50?
a. –0.0668
b. –0.9332
c. 0.0668
d. 0.9332
c. 0.0668
____ measure of how much distance is expected on average between a sample mean (M) and the population mean (μ).
Standard Error
Reject or Fail to Reject the null:
p<.05
Reject the null hypothesis
At what sample size the Central Limit Theorem hold true?
n= 30
A z-score of 0 is equal to the _________?
Population mean
______ requires that each individual in the population has an equal chance of being selected.
Random Sample
If a sample (n=50) was selected from a population with a mean with of 80, what would be the expected value of M?
80
Expected value of M = Population Mean
Power decreases/ increases as sample size increases.
Power decreases/ increases as standard error increases.
Increases
Decreases (inverse relationship)
____ is when you reject the null when you should have failed to reject the null.
Type 1 error
DOUBLE!!! 600 POINTS
How many eyes does a bee have?
Five
For a normal distribution with a mean of μ = 60 and a standard deviation of σ = 10, find the percentile rank for a score of:
x= 75
x= 31
93rd percentile
.2nd percentile
Which one has lower variance?
Distribution of means or distribution of scores
Distribution of means
If the probability of a type 2 error is 33%, what is beta?
What is the probability of Power?
Beta: 33%
Power: 67% (1-33%)
What does alpha, critical region and type 1 error have to do with one another?
The critical region is essentially the alpha, alpha tells you the likelihood of type 1 error.
Alpha sets the size of the critical region, and also tells us the probability we are willing to accept of committing a type 1 error.
Under what circumstances would a score that is 15 points above the mean be considered to be near the center of the distribution?
a. when the population mean is much larger than 15
b. when the population standard deviation is much larger than 15
c. when the population mean is much smaller than 15
d. when the population standard deviation is much smaller than 15
b. when the population standard deviation is much larger than 15
For a normal distribution with a mean of μ = 500 and σ = 100, what is the probability of selecting an individual with a score less than 400?
a. 0.1587
b. 0.8413
c. 0.34.13
d. –0.15.87
a. 0.1587
A random sample is obtained from a population with µ = 80 and σ = 10 and a treatment is administered to the sample. Which of the following outcomes would be considered noticeably different from a typical sample that did not receive the treatment?
a. n = 25 with M = 81
b. n = 25 with M = 83
c. n = 100 with M = 81
d. n = 100 with M = 83
d. n = 100 with M = 83
Larger mean difference= larger z-score
larger sample size= smaller SE= larger z-score
If a distribution is 85% overlapped, is the effect size big or small?
Small
If sample size increases what happens to critical regions?
NOTHING
On what test did you do the best?
Math test: Mean = 70, SD = 10
Your score = 85
History test: Mean = 80, SD = 5
Your score = 90
Math: 1.5
History: 2
Find each of the following probabilities for a normal distribution.
p(z > 1.25)
p(z > –0.60)
p(z < 0.70)
p(z < –1.30)
.1056
.7256
.2420
.0968
There are 620 public high schools in Texas. The mean number of students per school is 1,120. Suppose that the true population mean (μ = 1,120) and the population standard deviation (σ = 260) are known to the Texas Department of Education. They select a simple random sample of 40 high schools to estimate μ. The mean number of students in the sample is M = 1,175, with a sample standard deviation of s = 240.
a. The standard deviation of the distribution of sample means =
b. The standard or typical average difference between the mean number of students in the 620 high schools in Texas (μ = 1,120) and one randomly selected high school in Texas is
c. The standard or typical average difference between the mean number of students in the sample of 40 schools (M = 1,175) and one randomly selected school in that sample is
d.The standard or typical average difference between the mean number of students in the 620 high schools in Texas (μ = 1,120) and the sample mean of any sample of size 40 is
a. 41.1 (asking for standard error)
b. 260 (asking for population standard deviation)
c. 240 (asking for sample standard deviation)
d. 41.1 (also asking for standard error)
A high school teacher has designed a new course intended to help students prepare for the mathematics section of the SAT. A sample of n = 20 students is recruited to for the course and, at the end of the year, each student takes the SAT. The average score for this sample is M = 438. For the general population, scores on the SAT are standardized to form a normal distribution with μ = 500 and σ = 100.
Can the teacher conclude that students who take the course score significantly higher than the general population? Use alpha = .01.
z= -2.77 (on the wrong tail)
FAIL TO REJECT
A Cohen's d of .20 is approximately:
a. 1/5 of a Standard Deviation
b. 1/2 of a Standard Deviation
c. 1/3 of a Standard Deviation
1/5 of a Standard Deviation
1/5= .20