Is the lottery fair? Power ball is a multistate lottery in which players try to guess the numbers that will turn up in a drawing of numbered balls. One of the balls drawn is the "Powerball." Matching the number drawn on the Powerball increases one's winnings. In a 17 month period, the Power ball was drawn from a collection of 35 balls numbered 1 through 35. A total of 147 drawings were made. For the purpose of this exercise, we grouped the numbers in to five categories: 1-7, 8-14, and so on. If the lottery is fair, then the winning number is equally likely to occur in any category. Following are the observed frequencies. Test the hypothesis that each of the categories is equally likely. Use the 0.010 level of significance and the P-value method with the TI-84 Plus calculator. 15-21 22-28 29-35 35 Category 1-7 8-14 Observed 25 30 34 23 Send data to Excel

2. Forty-five percent of the entering CSUN freshmen in Fall 2019 were proficient in math. www.csun.edu/counts/new_first_time_freshman.php a. You want to see if the percentage is different for this fall's entering freshmen. Your hypotheses are Ho: На: where p stands for the percentage of freshmen who were proficient in Fall 2019 / this fall. b. Suppose that the null hypothesis is true that the percentage is 45% for this fall. Here is the sampling distribution of the values of p that would be expected if you repeatedly took random samples of 150 freshman entering this fall and found the proportion proficient in math. From the sketch alone, estimate the mean and the SE 0.33 0.37 0.41 0.45 0.49 0.53 0.57 If the null hypothesis is true, would it be unusual to get 50% in your sample who were proficient in mathematics? Explain: If the null hypothesis is true, would it be unusual to get 45 freshmen in your sample who were proficient in mathematics? Explain: c. You take a random sample of 150…

Find the P-value with z-score (1) if doing a right-tail hypothesis test

If a hypothesis test produces a z-score in the critical region, which decision should be made? O reject the alternative hypothesis ) fail to reject the alternative hypothesis ) reject the null hypothesis ) fail to reject the null hypothesis O O O 0