CHAPTER Paired Samples 25 PART 2 Can a

  • Slides: 11
Download presentation
CHAPTER Paired Samples 25 PART 2

CHAPTER Paired Samples 25 PART 2

Can a food additive increase egg production? Agricultural researchers want to design an experiment

Can a food additive increase egg production? Agricultural researchers want to design an experiment to find out. They have 100 hens available. They have two kinds of feed: the regular feed and the new feed with the additive. They plan to run their experiment for a month, recording the number of eggs each hen produces. Design an experiment that will require a two-sample t-test to analyze the results. Randomly assign 50 hens to each of the two kinds of feed. Compare the mean egg production of the two groups at the end of one month. R Group 1: 50 hens – regular a Compare n feed 100 hens d egg Group 2: 50 hens – additive o m production

Can a food additive increase egg production? Agricultural researchers want to design an experiment

Can a food additive increase egg production? Agricultural researchers want to design an experiment to find out. They have 100 hens available. They have two kinds of feed: the regular feed and the new feed with the additive. They plan to run their experiment for a month, recording the number of eggs each hen produces. Design an experiment that will require a matched-pairs t-test to analyze the results. Randomly divide the hens into two groups of 50 hens each. Feed the hens in the first group the regular feed for two weeks, then switch to the additive for two weeks. Feed the hens in the second group the additive for two weeks, and then switch to the regular feed for two weeks. Subtract each hen’s regular egg production from her additive egg production and analyze R the mean difference. Group 1: 50 hens – additive 2 a Analyze mean weeks then regular 2 weeks 100 hens nd difference in Group 2: 50 hens – regular 2 o egg weeks then additive 2 weeks m production

Values for the labor force participation rate of women are published by the U.

Values for the labor force participation rate of women are published by the U. S. Bureau of Labor Statistics. We are interested in whethere was a difference between female participation in 1968 and 1972, a time of rapid change for women. We check LFPR values for 19 randomly selected cities for 1968 and 1972. Shown below is software output for two possible tests. Which of these tests is appropriate for these data? State your conclusion based on the test that you chose. The paired t-test is appropriate Paired t-Test of µ(1 -2) Test Ho: µ(1972 -1968)=0 vs Ha: µ(1972 -1968)≠ 0 because the labor force Mean of Paired Differences = 0. 0337 participation rate for two different t-Statistic=2. 458 w/18 df years is paired by city. P=0. 0244 Since the P-value = 0. 0244, 2 -Sample t-Test of µ 1 -µ 2 there is evidence of a difference Ho: µ 1 -µ 2=0 Ha: µ 1 -µ 2 ≠ 0 in the average labor force Test Ho: µ(1972)-µ(1968)=0 vs Ha: µ(1972)-µ(1968) ≠ 0 participation rate for women Difference Between Means = 0. 0337 between 1968 and 1972. The t-Statistic = 1. 496 w/35 df evidence suggests an increase P=0. 1434 in the participation rate for women.

Having done poorly on their math final exams in June, six students repeat the

Having done poorly on their math final exams in June, six students repeat the course in summer school and take another exam in August. a) If we consider these students to be representative of all students who might attend this summer school in other years, do these results provide evidence that the program is worthwhile? b) If your conclusion is incorrect, what type of error was made? June 54 49 68 66 62 62 Augu 50 65 74 64 68 72 st

Step 1: State the hypotheses. *If scores have improved, then the August scores would

Step 1: State the hypotheses. *If scores have improved, then the August scores would be higher than the June scores, thus June – August would be negative. Alternatively, you could do August – June >0.

Step 2: State the conditions and model. üPaired data assumption: The scores are paired

Step 2: State the conditions and model. üPaired data assumption: The scores are paired by student. üRandomization condition: Assume that these students are representative of students who attend this school in other years. ü 10% condition: 6 students < 10% of all students üNormal population assumption: The histogram of differences between June and August scores shows a distribution that could come from a Normal population. Since the conditions are satisfied, the sampling distribution of the difference can be modeled with a t-model with 5 degrees of

Step 3: Mechanics

Step 3: Mechanics

Step 4: Conclusion Since the P-value of 0. 0699 is fairly high (higher than

Step 4: Conclusion Since the P-value of 0. 0699 is fairly high (higher than 0. 5) we fail to reject the null hypothesis. There is not enough evidence to conclude that scores increased on average. The summer school program does not appear worthwhile, but the P-value is low enough that we should look at a larger sample to be more confident in our conclusion.

b) If this conclusion is incorrect, what type of error was made? We concluded

b) If this conclusion is incorrect, what type of error was made? We concluded that there was no evidence of an increase and failed to reject the null. If this is wrong and there was an increase, this is a Type II error (mistakenly failing to reject the null).

Today’s Assignment q. Add to HW: page 602 #2, 3, 6, 21 q. Due

Today’s Assignment q. Add to HW: page 602 #2, 3, 6, 21 q. Due Thursday q. Quiz Friday q. Test #5 after Spring Break– Chapters 23, 24, 25 (Hypothesis testing for means)