SmalleyTylerStatsHomeworkWeek6

STA 144 Week 6 Homework Work on the following problem set from chapter 11 1. Using the data in the file named Chapter 11 Data Set 2 (in the appendix), test the research hypothesis at the .05 level of significance that boys raise their hand in class more often than girls. Do this practice problem by using SPSS or by hand. What is your conclusion regarding the research hypothesis? Remember to first decide whether this is a one or two-tailed test. a. It seems like in the first test, the value of p is just barely at about the significance level and does not warrant completely rejecting the null hypothesis as it is extremely close and perhaps further testing would be required because it cannot be said with certainty that one group is better at raising their hands than the other. However on the second test, the p value does have a significant enough higher value that might allow us to assume in that instance that boys raise their hands more often. 2. Using the same data set (Chapter 11 Data Set 2), test the research hypothesis at the . 01 level of significance that there is a difference between boys and girls in the number of times they raise their hand in class. Do this practice problem by using SPSS or by hand. What is your conclusion regarding the research hypothesis? You used the same data for this problem as for Question 1, but you have a different hypothesis (one is directional and the other is nondirectional). How do the results differ and why? a. The conclusion shows that there is definitely a difference among boys and girls when raising their hands during class. This is made clear from two different aspects. The first being that the significance level was made smaller and therefore easier to attain a higher value and therefore show a promising result. Also, making it a two tailed test means that there is not effort to prove a bias towards any one way and all that needs to be shown is that there is in fact a difference. 3. Time for some tedious, by-hand practice just to see if you can get the numbers right. Using the following information, calculate the t-test statistics by hand. a. X1 = 62 X2 = 60 n1 = 10 n2 = 10 s1 = 2.45 s2 = 3.16,,,,, T = 1.58173

b. X1 = 158 X2 = 157.4 n1 = 22 n2 = 26 s1 = 2.06 s2 = 2.59…. T = 0.876629 c. X1 = 200 X2 = 198 n1 = 17 n2 = 17 s1 = 2.45 s2 = 2.35… T = 2.55437 3. Using the results you got from Question 3, and a level of significance of .05, what are the two-tailed critical values associated with each? Would the null hypothesis be rejected? A – Critical Value is 2.1098, the null hypothesis would not be rejected B – Critical Value is 2.0141, the null hypothesis would not be rejected C – Critical Value is 2.0395, the null hypothesis would be rejected 4. Here’s a good one to think about. A public health researcher tested the hypothesis that providing new car buyers with child safety seats will also act as an incentive for parents to take other measures to protect their children (such as driving more safely, child-proofing the home, etc.). Dr. L counted all the occurrences of safe behaviors in the cars and homes of the parents who accepted the seats versus those who did not. The findings? A significant difference at the .013 level. Another researcher did exactly the same study, and for our purposes, let’s assume that everything was the same—same type of sample, same outcome measures, same car seats, and so on. Dr. R’s results were marginally significant (remember that from Chapter 9?) at the .051 level. Whose results do you trust more and why? a. I would trust Dr. R’s research results more as it appears that his significance level would have been harder to beat and by achieving it, would show that there is indeed some form of correlation between the habits of the driving and the implementation of the child safety seats within the car.

We want to test if students at our school score differently on a grammar test than the national population of readers (where μ = 89). We take a sample of ten (n=10) readers whose grammar reading scores are given below. Use this as a sample to do the other questions below. 72 67 59 76 93 90 75 81 71 93 1. State the RESEARCH Hypothesis or H1 a. The students at our school score differently on a grammar test than the national population of readers. 2. State the NULL Hypothesis or Ho a. H0: There is no difference in the scores of students at our school and the national population of readers 3. Identify H1 as one or two-tailed a. This is a two-tailed test 4. Specify alpha level (level of significance) a. Alpha level = .05 5. Specify Degrees of Freedom (n – 1) a. Degrees of freedom = 9 (note that SPSS will also give you this) 6. Identify Critical Value—(t crit ) from the t table (in the appendix) a. Critical value = +/- 2.262 7. Calculate t-score—( tobt ) using SPSS (this has been done for you and the results are given below: t obt= -3.118 One-Sample Statistics N Mean Std. Deviation Std. Error Mean Grammar 10 77.70 11.461 3.624 One-Sample Test Test Value = 89 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper Grammar -3.118 9 .012 -11.300 -19.50 -3.10

8. State decision (rejection) rule –use the diagram of the normal distribution curve a. If the calculated t is beyond the t crit, then the NULL is rejected b. If the calculated t not beyond the crit, then there is a FAILURE to reject the NULL If t obt is beyond 2.262 in the right tail or beyond -2.262 in the left tail, we have a rejection of the null hypothesis and we can accept the research hypothesis. 9. State the meaning of the results, explain the outcome, and draw a conclusion. T obt is beyond t crit in the left tail; therefore, reject the null hypothesis; the reading scores of children in our school are lower than the scores of the national population. They are significantly lower. Note: SPSS will always calculate significance on a two-tailed test. If you have a one-tailed test you will need to take t crit from the tables. 8. The population mean  on a national scholastic achievement test is 100 with a standard deviation of 30. The students in Mr. Smart’s class got the following scores: 127 121 123 128 118 126 120 130 128 119 127 125 Using the criterion of 0.05 in the upper tail only, determine if Mr. Smart’s class is representative of the population. 1. State the RESEARCH Hypothesis or H1 a. Mr. Smart’s classroom tests differently on their tests than the national average 2. State the NULL Hypothesis or Ho a. There is no difference between nationwide scores and Mr. Smart’s classroom 3. Identify H1 as one or two-tailed a. This is a two tailed test. 4. Specify alpha level (level of significance ) a. The level of significance is 0.05 5. Specify Degrees of Freedom (n – 1) a. Df = 11 6. Identify Critical Value—(t crit ) from the t table (in the appendix ) a. Critical value = 1.7959 7. Calculate t-score—( tobt ) using SPSS (this has been done for you and the following printout shows the analysis of the data. a. 21.33

b. Research Hypothesis = there may be a difference in how a policeman is able to resolve conflict based on whether or not they completed sensitivity training. c. Using an alpha = 0.05, what is t ( crit )? a. t = 1.8331 d. Using SPSS, calculate t ( obt ) a. e. What should you conclude?