Week 6: Sunday MOM Homework Assignment Hypothesis Testing with Name: Vanessa Russell Two Samples Exercises are set up so you can try the problem twice, then the answer will be shown on your third attempt. If you miss a problem on the exercises and want to improve your score, you can "Try a similar problem", which will give you a new question of the same type. You can keep on working on versions of a question until you get a perfect score on the exercises. #1 Points possible: 2. Total attempts: 3 Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level. The null and alternative hypothesis would be: H0 : p M = p F H1 : p M p F H 0 : M = F H 1 : M > F H0 : p M = p F H1 : p M < p F H 0 : M = F H 1 : M F The test is: righttailed twotailed lefttailed Based on a sample of 20 men, 40% owned cats Based on a sample of 80 women, 45% owned cats The test statistic is: The pvalue is: Based on this we: Reject the null hypothesis Fail to reject the null hypothesis (to 2 decimals) (to 2 decimals) H 0 : M = F H 1 : M < F H0 : p M = p F H1 : p M > p F #2 Points possible: 2. Total attempts: 3 For each scenario listed on the left, determine whether the scenario represents an Indepenent Samples or Matched pairs situation by placing the appropriate letter in the box provided. Comparing pain levels before and after treatment with magnetic therapy Comparing pretest scores before training to posttest scores Comparing the number of speeding tickets received by men to the number received by women Comparing pain levels of a group receiving a placebo to a group receiving a medicine a. Independent Samples b. Matched Pairs #3 Points possible: 2. Total attempts: 3 A teacher is experimenting with a new computerbased instruction and conducts a study to test its effectiveness. In which situation could the teacher use a hypothesis test for matched pairs? The teacher gives each student in the class a pretest. Then she teaches a lesson using a computer program. Afterwards, she gives each student a posttest. The teacher wants to see if the difference in scores will show an improvement. The teacher randomly divides the class into two groups. One of the groups receives computerbased instruction. The other group receives traditional instruction without computers. After instruction, each student takes a test and the teacher wants to compare the performance of the two groups. The teacher uses a combination of traditional methods and computerbased instruction. She asks students which they liked better. She wants to determine if the majority prefer the computerbased instruction. #4 Points possible: 2. Total attempts: 3 5.32 Fuel efficiency of manual and automatic cars, Part I: Each year the US Environmental Protection Agency (EPA) releases fuel economy data on cars manufactured in that year. Below are summary statistics on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions manufactured in 2012. Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage? Assume that conditions for inference are satisfied. Mean SD n City MPG, Automatic 16.12 3.58 26 City MPG, Manual 19.85 4.51 26 The hypotheses for this test are: Ho: automatic = manual Ha: automatic < manual Ho: automatic = manual Ha: automatic > manual Ho: automatic = manual Ha: automatic manual The test statistic is: (please round to two decimal places) The pvalue is: (please round to four decimal places) Interpret the result of the hypothesis test in the context of the problem: The data provide sufficient evidence that there is a difference between the average fuel efficiency of manual and automatic cars in terms of their average city mileage The data do not provide sufficient evidence that there is a difference between the average fuel efficiency of manual and automatic cars in terms of their average city mileage The data provide sufficient evidence that there is no difference between the average fuel efficiency of manual and automatic cars in terms of their average city mileage #5 Points possible: 2. Total attempts: 3 You wish to test the following claim (H ) at a significance level of = 0.002. For the context of this problem, = P ostT est P reT est where the first data set represents a pretest and the second data set represents a posttest. (Each row represents the pre and post test scores for an individual. Be careful when you enter your data and specify what your and are so that the differences are computed correctly.) a d 1 H H 2 o : d = 0 a : d 0 You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: pretest posttest 71.3 67.1 92.6 97.1 76.4 80.5 57.5 58.3 81.8 70.6 27.4 19.2 31.2 31.8 40.3 27.4 65.4 57.7 59.6 52.1 58.2 48.8 56.8 35.1 63.2 68.1 76.4 67.7 65.4 75.3 80.7 74.7 54.6 51.7 53.8 45.4 48.2 35.6 35.5 41.3 What is the test statistic for this sample? test statistic = (Report answer accurate to 4 decimal places.) What is the pvalue for this sample? pvalue = (Report answer accurate to 4 decimal places.) The pvalue is... less than (or equal to) greater than This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the mean difference of posttest from pretest is not equal to 0. There is not sufficient evidence to warrant rejection of the claim that the mean difference of posttest from pretest is not equal to 0. The sample data support the claim that the mean difference of posttest from pretest is not equal to 0. There is not sufficient sample evidence to support the claim that the mean difference of posttest from pretest is not equal to 0