Problems
What is the Z score for the following sampling distribution?
Mean: 50, X:65, Standard Deviation: 10, n: 100
15
What does it mean for a statistic to be unbiased?
A statistic is said to be unbiased if the statistic is the same as the parameter it estimates for.
Draw and label a normal distribution with:
Mu: 75
Sigma: 10
Skyler will have to check :)
What is the Z score approximation formula?
x-pn / √npq
Write the null hypothesis for a study testing to see if a sample of students are above average in IQ.
Ho: µ≤100
What is the probability of getting exactly 4 successes in 5 trials with p=0.7?
0.360
What is a sampling distribution?
A sampling distribution is the distribution that would be formed when you when you take an infinite number of samples of some size n, calculate the statistic, and put those on their own distribution.
If I am looking for the middle 80% of a distribution, what 2 Z scores would cut off my tails?
-1.25 & 1.25
What is the formula for Cohen's d?
M - µ
_____
σ
When writing hypotheses, the equal sign always goes in which hypothesis?
Null.
Leslie is running a study to determine if the 45 rats in her sample are faster than the average rat (µ=2.75 ft/sec, σ=.17ft/sec). After testing her rats, she finds they run at an average speed of M=2.9 ft/sec. She calculates a Z score for her sample data and makes a decision. Determine what that decision is and then calculate the probability that she made a Type I error.
Reject; 5%
What does the Central Limit Theorem state?
The CLT states that as a sample size n approaches infinity, the sampling distribution of the mean will approach a normal distribution with a mean of µ and a standard deviation of σ / √ n
What are the small, medium, and large effect sizes for Cohen's d?
Small: .2
Medium: .5
Large: .8
What is the Z score formula for a sampling distribution?
X-Mu / Sigma/√ n
What are the requirements to meet the CLT?
N >= 30
Daren draws a sample of 58 males from the population of adult males who are known to have the following average weight (µ=200, σ=30). Daren calculates the average weight of the males in his sample to be 195 with a sample standard deviation of 40 pounds. What is the probability of obtaining this average weight or less if the males in Daren’s sample are representative of the average male population?
10.2%
What is the best & worst way to increase power?
Best: Increase sample size
Worst: Increase significance level
Which of the following is NOT a characteristic of the binomial distribution?
The trials are independent.
Each trial has exactly two possible outcomes.
The probability of success remains constant for each trial.
The trials are dependent.
The trials are dependent.
What is the P(X) formula?
N!
__________ P^X P^ (N-X)
X!(N-X)!
What is a type 1 error & type 2 error? Define and give an example.
Type 1: Reject a correct Null
Type 2: FTR an incorrect Null
Gerard suspects that his clients are lower in self-esteem than people in the general population (µ=34, σ=7.8). He gives a sample of 98 clients a self-esteem test and finds that they scored M=35.7. Do the data support his suspicion?
No, our data are in the wrong tail
What is alpha / significance level?
The probability at which we reject assumptions and support alternative hypothesis.
IOW: The probability of rejecting the null when the null is actually true.
Assuming a normal distribution, what is the probability of scoring a Z score between 0.60 and 1.96?
0.2493
What is the formula for standard error?
σ / √n
What happens to standard error as sample size increases?