Measures of central tendency
This is something that is also known as the average
What is the mean?
This is the definition of measures of dispersion?
What is a way to measure the spread of the distribution?
This is the act of specifying an expected result of a study assuming the null hypothesis is true.
What is hypothesis testing?
Suppose an investigator wants to know whether the mean IQ scores of school teachers, differs from the mean IQ scores of the general population. We know the mean IQ score for the general population = 100. The population standard deviation is 25. The sample size is 50. The mean IQ for the school teachers is 132. Use an alpha level of 0.05. State your critical values.
What are + 1.96 and - 1.96? These are the critical values because the alpha level 0.05 and the test is two-tailed, meaning that the 5% (given by the alpha level) that the null would have to fall outside for us to reject the null, would be split between both tails, so 2.5% for each tail. If you use the z-table the 0.025 past z would correspond to + or - 1.96
This is an indicator that the you will use a t-test instead of a z-test.
What is no σ?
This is something that occurs most often and may or may not fall in the middle
What is mode?
This dictates the shape of the bell curve?
What is the spread of scores?
This states that a Population has a mean & a sampling distribution of sample means will also have a mean. Those means will be equal. A Population has a standard deviation, & a sampling distribution of sample means also has a standard deviation, but they are not equal and one would need to calculate the standard error of the mean.
What is the central limit theorem?
Suppose an investigator wants to know whether the mean IQ scores of school teachers, differs from the mean IQ scores of the general population. We know the mean IQ score for the general population = 100. The population standard deviation is 25. The sample size is 50. The mean IQ for the school teachers is 132. Use an alpha level of 0.05. State your reasoning for choosing your critical values.
What is these are the critical values are - and + 1.96 because the alpha level is 0.05 and the test is two-tailed, meaning that the 5% (given by the alpha level) that our result would have to fall outside for us to reject the null, would be split between both tails, so 2.5% for each tail, and if you use the z-table the 0.025 past z would correspond to + or - 1.96?
This is the formula where the correction for t-tests is made and this is the correction.
What is variance? What is SS/N-1 instead of SS/N
Given a set of data, this is the point where 50% falls above and 50% falls below
What is median?
These are the types of dispersion.
What are range, average deviation, sums of squares, variance, and standard deviation?
This is the statement of no difference: sample and population means are the same.
What is the null hypothesis?
Suppose an investigator wants to know whether the mean IQ scores of school teachers, differs from the mean IQ scores of the general population. We know the mean IQ score for the general population = 100. The population standard deviation is 25. The sample size is 50. The mean IQ for the school teachers is 132. Use an alpha level of 0.05. Conduct a one-sample z test to test the hypothesis that μ=100 (two-tailed). What is your standard error of the mean?
What is 3.54?
There is more than one formula for t-tests where we make a correction to give us an estimate as close as possible to the actual standard deviation. True or False.
What is false, we only make the correction for variance?
These are the three types of measures of central tendency?
What are the mean, median, and mode?
This represents the number of standard deviation units that a score falls - above or below - the mean.
What is a z-score?
Suppose an investigator wants to know whether the mean IQ scores of school teachers, differs from the mean IQ scores of the general population. We know the mean IQ score for the general population = 100. The population standard deviation is 25. The sample size is 50. The mean IQ for the school teachers is 132. Use an alpha level of 0.05. What are the steps to solve this problem?
What is stating the null and alternative hypotheses, stating the alpha level and using it to find the critical values, calculating the standard error of the mean, calculating the z observed (or t observed, in some cases), and rejecting or failing to reject the null?
Suppose an investigator wants to know whether the mean IQ scores of school teachers, differs from the mean IQ scores of the general population. We know the mean IQ score for the general population = 100. The population standard deviation is 25. The sample size is 50. The mean IQ for the school teachers is 132. Use an alpha level of 0.05. What is your z-observed?
What is 9.04?
A professor gave students a mini-informal (not for points quiz) to her 11 students at the beginning of the semester. This quiz was a national quiz given by professors to their own students, to see how they would do on on the GRE if they took it today. The scores below are out of 20. The population mean is 10. Use an alpha level of 0.05. Do a two-tailed test to see how the class compared to the national mean. Calculate mean, sums of squares, variance, and standard deviation. Are these estimates or not? What are the critical values (how do you get this)?
2,6,10,4,5,18,20,2,2,5, 4
What is variance, standard deviation, and t observed are, but sums of squares is not?
The critical values are +2.228 and -2.228.
Mean: 7.09
Sums of squares: 400.91
Variance: 40.091
Standard Deviation: 6.396
Given the following data, calculate mean, median, and mode:
2,6,10,4,5,18,20,2,2,5,4.
Mean: What is 7.09?
Median: What is 5?
Mode: What is 2?
Given the following data, calculate sums of squares, variance, and standard deviation. Hint: Write down the formulas first and then plug and chug.
Data: 2,6,10,4,5,18,20,2,2,5,4
Sums of squares: What is 400.91?
Variance: What is 36.45?
Standard deviation: What is 6.04?
Suppose an investigator wants to know whether the mean IQ scores of school teachers, differs from the mean IQ scores of the general population. We know the mean IQ score for the general population = 100. The population standard deviation is 25. The sample size is 50. The mean IQ for the school teachers is 132. Use an alpha level of 0.05. State the null and alternative hypothesis.
Null H0: μ = x̅ or μ = 100
Alternative: H1: μ ≠ x̅ or μ ≠ 100
Note: Sometimes, the alternative can be directional, as in it could be > or <, if the question is one tailed and a direction is predicted. Can someone give me an example of how we can change this question into a one tail/directional test?
Suppose an investigator wants to know whether the mean IQ scores of school teachers, differs from the mean IQ scores of the general population. We know the mean IQ score for the general population = 100. The population standard deviation is 25. The sample size is 50. The mean IQ for the school teachers is 132. Use an alpha level of 0.05. Conduct a one-sample z test to test the hypothesis that μ=100 (two-tailed). Do you reject or fail to reject the null?
What is we reject the null because our value is +9.04 which falls much beyond our critical values of - and + 1.96?
A professor gave students a mini-informal (not for points quiz) to her 11 students at the beginning of the semester. This quiz was a national quiz given by professors to their own students, to see how they would do on on the GRE if they took it today. The scores below are out of 20. The population mean is 10. Use an alpha level of 0.05. Do a two-tailed test to see how the class compared to the national mean. Calculate the estimated standard error of the mean and t observed. Do you fail to reject or reject the null?
2,6,10,4,5,18,20,2,2,5, 4
Estimated standard error of the mean: 1.928
t observed: -1.51
Since our critical values are - and + 2.228 and our t observed falls in between this range, we fail to reject the null. This indicates that the difference in means is due to sampling error.