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Make sure to save often to avoid losing work! You ask 12 people how much they like pizza on a scale from 1 to 7, where 7 is highly enjoyable and 1 is not enjoyable. Then, you make them eat a pizza for dinner every day for two weeks. After that, you ask them how much they like pizza. Before the study, you observe the values: 7 7 3 1 6 5 4 3 3 4 6 7 After the study, you observe the values: 2 1 4 4 1 1 2 1 6 4 5 4 3. Examine the means and SDs for each of the groups 3.
Do you reject or fail to reject the null? Cannot use external packagesPlease see lecture notes below provided by professor to do lab homework above, and to follow their packages and formulas please Lab 9-Contents Lecture Notes 1. Comparing Independent Groups 2. The T-test: The influence of differences in the Means 3.
The T-test: The influence of differences in the Variance 4. The T-test: The influence of differences in Skewness 5. Comparing Dependent Groups: The Paired T-test Goal: In this lab we will look at comparing independent and dependent groups in R 1. Comparing Independent Groups Previously we learned the function t. We can extend our knowledge of this function for using it to compare 2 independent groups. All we need to do is to add another variable to the function Two ways to perform an Indepedent Sample t-test in R: t.
In Chapter 9, you learned two types of two-sample t tests: 1 Student's two-sample t-test assumes variance is equal 2 Welch's test assumes variance is NOT equal The function t. Let's assume that I measured 20 young people and 25 old people on some measure could be anything Similarly, we need to decide if we're going to use the student's t-test or the welch's t-test.
NOTE: we simulated the data so that the variance would be equal, so we'll presume that the student t-test is fine. Thought Question 1: Given all that we've just discussed, what does it mean to reject the null hypothesis using our t. The T-test: The influence of differences in the Means Let's first load the table object lab9.
B Look histograms of the three variables. C Based on what you saw in A , what are the differences between these 3 variables?
What conclusion can you make based on the results from the two t-tests? In other words, how does the difference in Means between two samples affect our t-test result assuming other things e. See Figure 9. In other words, how does the difference in variance between two samples affect our t-test result assuming other things e. Problems with controlling the probability of a Type I error occur: It can yield inaccurate confidence intervals when sampling from normal distributions with unequal sample sizes and unequal variances.
The T-test with Trimmed Means: Yuen's T As we saw above, skewness can have an influence on our ability to detect statistical significance. Given what we've just seen, how might skewness affect the results we get?
Comparing Dependent Groups: The Paired T-test We just learned the various ways to conduct a t-test for independent groups ie. We used Student's t-test, Welch's, and Yuen's. Now we are going to learn about what to do when our groups are dependent ie.
Often the dependent groups we see are based on time, such that people are measured at baseline group1 and we want to see how much they've changed at followup group2. Here is an example: We are interested in measuring the weight of college freshmen before and after the first year to test whether or not there is any truth to the "freshman 15"? We tested 16 freshmen on the first day of school, and tested them again after finals week of the spring semester.
The data is recorded in a table in frosh. The formula for calculating a paired t-test in R is again t. Let's find out by running the normal independent samples T-Testt.
One company monitors the accuracy of the scanner by randomly sampling packages and verifying that each package has been correctly scanned. Sample Size, n Number Correctly Scanned 25 To complete this activity, use Excel to:Calculate the sample proportion for each sample size. Calculate the single-proportion sampling error for each sample size. Submit your work Excel file.
The Lazer Company has developed a process that will meet the specifications with respect to the standard deviation, but it is still trying to meet the mean specifications. A test run considered a random sample of parts was produced, and the company wishes to determine whether this latest process that produced the sample will produce parts meeting the requirement of an average diameter equal to 6 inches. Use Excel to:Construct the appropriate null and alternative hypotheses with correct parameters.
Develop the decision rule assuming that the sample size is parts and the significance level is 0. In a Word document:Recommend what the Lazer Company should conclude if the sample mean diameter for the parts is 6. Submit your recommendations in a Word document and attach your Excel file.
What is? Find the limit of the function by using direct substitution 4 points Does not exist If and , then. Find the limit of the function algebraically. Find the equation of the horizontal asymptote for the function,.
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