Stats test 2
Probability and proportion ARE THE SAME THING! Here's an example...
"what is the probability of selecting an individual with an IQ of less than 120?" "what proportion of all the individuals in the population have IQ score of less than 120?" -SAME QUESTION
A score that is 12 points below the mean corresponds to a z-score of z = -1.50. What is the standard deviation?
**Standard deviation = 12/1.50 **ANSWER: 8 pts. In this case, don't worry about the negative sign. Just divide the two and pick the positive answer. That is, 8.
Goal of inferential statistics
-Begin with a sample and then answer general questions about the population -two-stage process
In general, the larger the sample size....
-The CLOSER the sample mean should be to the population mean -means obtained from smaller samples with be scattered further away from the mean
percentile rank vs. percentile
-same thing -70% = 70th percentile rank
for the hypothesis test to conclude that the treatment does have an effect....
-the sample data must be in the critical region! -the sample data should be in the critical region!
Probability
-used to predict the types of samples that are likely to be obtained from a population -connection between samples and population (inferential statistics rely on this)
What information is provided by the (+/-) sign of a z score?
-whether or not the score is above or below the mean
what's the largest permissible alpha value?
.05
What is required for an Independent Random Sample?
1. Each member of the population must have an equal chance of selection. 2. The members are selected randomly instead of voluntarily selecting themselves.
it is known that IQ scores from a normal distribution with u = 100, and q = 15. Given this information, what is the probability of random selecting individual with an IQ score of less than 120?
1. find z-score (120-100/15 = 1.33) 2. then, look up the z-score value in the unit normal table, go to the body column (b) and find .9082 3. p(x < 120) = p(z < 1.33) = .9082 or (90.82%) -Thus, an IQ score of x = 120 corresponds to a z-score of 1.33 and IQ score less than 120 also correspond to a z-score of 1.33
sampling distribution
A distribution of statics obtained by selecting ALL POSSIBLE SAMPLES of a specific size from a population
what is the consequence of increasing the alpha level? (.01-.05)
It will increase the likelihood of rejecting the null hypothesis (Ho) and increase the risk of a type 1 error
For a population with a standard deviation of q = 14, a score of x = 24 corresponds to z = -0.50. What is the population mean (u)?
Mean formula : u = x- zq u = 24 - (-0.50)(14) u = 31
If a question asks you to find X, it's asking you to find the... (formula?)
RAW SCORE x= u + zq
Type 1 error (alpha)
Rejecting null hypothesis when it is true
A score that is 20 points above the mean corresponds to a z-score of z = 1.25. What is the standard deviation?
Standard deviation = 20/1.25 ANSWER: 16 pts.
For a population with a mean of u = 45, and a score of X = 54 that corresponds to a z-score of z = 1.50. What is the standard deviation (q)?
Standard deviation formula: q = X- u/ z q = 54-45/1.50 q = 6
What information is provided by the magnitude (numerical value) of the z-score?
Tells you how many standard deviations the associated value of x is from the mean. (x = 45)
distribution of sample means
The collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population -CONTAINS ALL POSSIBLE SAMPLES
smapling error
The natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter
What is a z-score?
The number of standard deviations away from the mean EX: z = -1.50 This means that the corresponding score is located below the mean by a distance of 1.50 standard deviations.
Type 2 error (beta)
accepting the null hypothesis when it is false
random smapling
each individual in the population has an equal chance of being selected
Formula for q (standard deviation)
q = x- q/ z
as the alpha level gets smaller...
the distance from the mean gets larger/tougher to reach
For a sample with a standard deviation of q = 6, X = 30, and z = -1.50. What is the mean?
u = X - zq u = 30 - (-1.50)(6) u = 39
Formula for U (MEAN)
u = x - zq
