UNIT 6 CHAPTERS 23,24,25 By Courtney and Ayla

CHAPTER 23 In this chapter we discuss the true means of one scenario. We compare a given mean for a scenario and a true mean that we find based on the data given. We must test an hypothesis and state our conditions: The Ho is always Ho:m= and Ha is either Ha:m, depending on what the question is asking you (m Is the mean given) The conditions are; Random, Independent, <10%, and the histogram of the graph must be nearly normal. If it is a little off its okay, just state that and continue on with the experiment.

23 CONTINUED

EXAMPLE: Textbook authors must be careful that the reading level of their book is appropriate for the target audience. Some methods of assessing reading level require the average word length. We’ve randomly selected 20 words from a randomly selected page in Stats: Modeling the World and counted the number of letters in each word: 5, 5, 2, 11, 1, 5, 3, 8, 5, 4, 7, 2, 9, 4, 8, 10, 4, 5, 6, 6 1.Suppose that our editor was hoping that the book would have a mean length of 6.5 letters. Does this sample indicate that the authors failed to meet this goal? Test an appropriate hypothesis and state your conclusion. 2.For a more definitive equation of reading level the editor wants to estimate the text’s mean word length to within 0.5 letters with a 98% confidence. How many randomly selected words does she need to use?

CHAPTER 24 In this chapter we discuss comparing two groups of data side by side. This comparison is similar to comparing two proportions, however we are comparing two means. We must test an hypothesis and state our conditions: The Ho is always Ho:M 1 – M 2 = 0 set of data and Ha is either Ha:M 1- M 2 is 0, depending on what the question is asking you. (m Is the mean given) The conditions are; Random, Independent, <10%, and the histogram of the graph must be nearly normal. If it is a little off its okay, just state that and continue on with the experiment.

CHAPTER 24 CONTINUED

EXAMPLE: A randomly sample of 13 men and 19 women in a college class reported their grade point averages (GPA’s). The histograms were nearly normal. Summary of statistics for these data are: 1.A women in the class says that she believes that the college women tend to have higher GPA’s then do college men. Does this sample support her claim? Test an appropriate hypothesis and state your conclusion. 2.Create and interpret a 95% confidence interval. Men Women

CHAPTER 25 In this chapter we discuss comparing the difference of means in a before and after situation We must test an hypothesis and state our conditions: The Ho is always Ho: M1 = 0 set of data and Ha is always Ha:M≠0, (m Is the mean given) The conditions are; Random, Independent, <10%, and the histogram of the graph must be nearly normal. If it is a little off its okay, just state that and continue on with the experiment.

CHAPTER 25 CONTINUED We are usually given the differences in the data, but if we are just given the before and after scenarios we can plug it into our list and spreadsheets and find the differences. Since we are still looking at means, we use the T interval, and we must find the T value. The formula for this is Tn-1( μ, SE) μ is the mean, and it is always 0 for this situation. SE is standard error, the formula is SE= σ /√n Degrees of freedom n-1 We use the Tcdf formula to solve this type of problem. Tcdf(lower bound, SE, degrees of freedom)

CHAPTER 25 CONTINUED Most people are definitely dominant on one side of their body – either right or left. For some sports being able to use both sides is an advantage, such as batting in baseball or softball. In order to determine if there is a difference in strength between the dominant and non-dominant sides, a few switch-hitting members of some school baseball and softball teams were asked to hit from both sides of the plate during batting practice. The longest hit (in feet) from each side was recorded for each player. The data are shown in the table at the right. Does this sample indicate that there is a difference in the distance a ball is hit by batters who are switch-hitters? 1. Test an appropriate hypothesis and state your conclusion

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