Hypothesis testing
What is alpha?
______________ _____ ____________________ describe the number of scores in a sample that are independent and free to vary.
What are degrees of freedom?
The collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population is called what?
What is the distribution of sample means?
Finding z-scores assumes that a distribution is ______________.
What is normal/typical?
How many siblings does Mattison have?
What is 2?
The _____________ hypothesis states that there is no change, difference, or relationship in the general population.
What is null?
A _______-score uses information about the standard error or deviation of the population, whereas a ______-score uses information about the estimated error or deviation of a sample.
What is z- and t-?
Sales representatives at a cellular phone retailer sell a mean of µ=200 and a standard deviation of σ=50 smartphones per year. At the Rochester, New York, branch, n=25 representatives sell M=220. Compute the z-score for the Rochester branch.
σm=σ/√n=50/√25=50/5=10
Z=M-µ/σm=220-200/10=20/10=2
Z=+2.00
The ____________ for a distribution is the sum of the scores divided by the number of scores.
What is mean?
If you've been in class, you know that the alpha symbol looks like a ______________ _________________ ________________.
What is backwards Jesus fish?
In most research, we reject the null hypothesis if p<______.
Find the t-value that forms the boundary of the critical region in the right-hand tail for a two-tailed test with α=.05 for a sample size of n=9.
df=8 and critical t=2.306
What is 2.306?
If the population standard deviation is σ=24, how large a sample is necessary to have a standard error that is equal to 6 points?
σm=σ/√n
What is n=16?
What is the mean and standard deviation of an IQ test?
What is 100 and 15?
Kylie works at what Mayville establishment?
What is Dollar General?
A random sample is selected from a normal population with a mean of µ=20 and a standard deviation of σ=10. After a treatment is administered to the individuals in the sample, the sample mean is found to be M=25. If the sample consists of n=25 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α=.05.
Critical region=z=+-1.96
σm=σ/√n=10/√25=10/5=2
z=M-µ/σm=25-20/2=5/2=+2.5
What is reject the null hypothesis; z falls in the critical region?
A random sample of n=7 individuals is selected from a population with µ=50, and a treatment is administered to each individual in the sample. After treatment, the following scores are observed:
37 49 47 47 47 47 43 45
What is the standard error for M and what is T?
M=45, µ=50, df=6, SS=96, s=4
Sm=√s2/n=√16/7=1.51
t=-5/1.51=3.31
What is 1.51 and -3.31?
Suppose that a professor randomly assigns students to study groups of n=4 students. The final exam in the professor's class has a µ=75 and a standard deviation of σ=10. What is the expected value of the mean and the standard deviation of the distribution of study group means?
What is = 75 and σm=σ/√n=10/√4=10/2=5
What is 75 and 5?
What is calculated by taking the sum of squared deviations and dividing it by the number of scores?
What is variance?
What is Tyler's middle name?
What is Jameson?
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 for the course and, at the end of the year, each student takes the SAT. The average score for this sample is M=562. 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 a one-tailed test with α=.01
Critical region for z +-2.33
σm=σ/√n=100/√20=100/4.47=22.37
z=M-µ/σm=562-500/22.37=+2.77
What is reject the null hypothesis, the z-score is in the critical region?
To evaluate the effect of a treatment, a sample is obtained from a population with a mean of µ=40 and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M=44.5 with a variance of s2=36. If the sample consists of n=4 individuals, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α=.05?
Critical t=3.182
Sm=√s2/n=√36/4=3
t=4.5/3=1.5
What is accept null hypothesis, t is short of critical region?
A population has a mean of µ=30 and a standard deviation of σ=8. If the population distribution is normal, what is the probability of obtaining a sample mean greater than M=32 for a sample of n=4?
σm=σ/√n=8/√4=8/2=4
z=M-µ/σm=32-30/4=2/4=.5
p(M>32)=.3085
What is calculated by taking the square root of the variance?
What is standard deviation?
What is Lily's major AND minor?