Stats HW 3

Stats HW 3- 5.51, 5.54, 6.16, 6.28, 6.54, 7.48, 8.12, 8.46 5.51- Null hypotheses and research hypotheses: For each of the following studies, cite the likely null hypothesis and the likely research hypothesis. a. A forensic cognitive psychologist wondered whether repetition of false information (versus no repetition) would increase the tendency to develop false memories, on average. - The null hypothesis is there is no connection between repetition and the tendency to develop false memories - The research hypothesis is the positive connection between repetition and the tendency to develop false memories b. A clinical psychologist studied whether ongoing structured assessments of the therapy process (versus no assessment) would lead to better outcomes, on average, among outpatient therapy clients with depression. - The null hypothesis is there is no connection between the outcome of structured assessment or the outcome of patients without an assessment - The research hypothesis is a better outcome for those with structured assessments than those without c. A corporation recruited an industrial-organizational psychologist to explore the effects of cubicles (versus enclosed offices) on employee morale. - The null hypothesis is the enclosed office employee morale - The research hypothesis is employee morale of a cubicle d. A team of developmental cognitive psychologists studied whether teaching a second language to children from birth affects children’s ability to speak their native language. -The null hypothesis is the children’s ability to speak their native language independent of teaching a second language - The research hypothesis is the children’s ability to speak their native language dependent of teaching a second language 5.54- Rejecting versus failing to reject an invitation: Imagine you have found a new study partner in your statistics class. One day, your study partner asks you to go on a date. This invitation takes you completely by surprise, and you have no idea what to say. You are not attracted to the person in a romantic way, but at the same time you do not want to hurt his or her feelings. a. Create two possible responses to the person, one in which you fail to reject the invitation and another in which you reject the invitation. - I enjoy being able to study together, but I would prefer to remain study partners. - Yes, I will go out with you but as friends. b. How is your failure to reject the invitation different from rejecting or accepting the invitation? - Even though the person doesn’t want to reject the invitation, they still don’t want to go out on the date but they do anyways. 6.16- A population has a mean of 250 and a standard deviation of 47. Calculate z scores for each of the following raw scores: a. 391 391z=(391-250)/47=3.0 b. 273 273z= (273-250)/47= 0.49 c. 199 199z= (199-250)/47= -1.09 d. 160 160z= (160-250)/47= =1.91 6.28- Compute the standard error (M) for each of the following sample sizes, assuming a population mean of 100 and a standard deviation of 20: a. 45 20÷45=2.98 b. 100 20÷100=2 c. 4500 20÷4500=0.30 6.54- Rural friendships and the General Social Survey: Earlier, we considered data from the GSS on numbers of close friends people reported having. The mean for this variable is 7.44, with a standard deviation of 10.98. Let’s say that you decide to use the GSS data to test whether people who live in rural areas have a different mean number of friends than does the overall GSS sample. Again, treat the overall GSS sample as the entire population of interest. Let’s say that you select 40 people living in rural areas and find that they have an average of 3.9 friends. a. What is the independent variable in this study? Is this variable nominal, ordinal, or scale? People living in rural areas; nominal b. What is the dependent variable in this study? Is this variable nominal, ordinal, or scale? Number of friends; nominal c. What is the null hypothesis for this study? H0:12; no change between the different groups d. What is the research hypothesis for this study? H0:12; the people do not have the same mean number of friends as general people e. Would we compare the sample data to a distribution of scores or to a distribution of means? Explain. No; the sample data needs to be compared to a distribution of means, scores means population 7.48- The Graded Naming Test and sociocultural differences: Researchers often use z tests to compare their samples to known population norms. The Graded Naming Test (GNT) asks respondents to name objects in a set of 30 black-and-white drawings. The test, often used to detect brain damage, starts with easy words like kangaroo and gets progressively more difficult, ending with words like sextant. The GNT population norm for adults in England is 20.4 Roberts wondered whether a sample of Canadian adults had different scores than adults in England. If they were different, the English norms would not be valid for use in Canada. The mean for 30 Canadian adults was 17.5. For the purpose of this exercise, assume that the standard deviation of the adults in England is 3.2. a. Conduct all six steps of a z test. Be sure to label all six steps. Step 1- - Population 1: GNT respondents to name objects in a set of 30 black and white drawings - Population 2: All GNT respondents - Comparison distribution: standard normal distribution of means - Assumption 1: The dependent variable is on a scale measure: Met - Assumption 2: Participants are randomly selected: sample was convenient because they were chosen from specific countries - Assumption 3: Population distribution is approximately normal: do not know if this is met since the sample size is 30 Step 2 -The null hypothesis was that people from England who did GNT would have the same results as those from Canada. H0:1=2 - The research hypothesis is that people from England who did GNT would have different results as those from Canada. H0:12 Step 3 M==20.4 ?M=?N=3.230=0.58 Step 4 =.05; Two-tailed, find the value that cuts the extreme 2.5% off both positive and negative tails .052=0.03 Critical value is 1.96 Step 5 z=M-??M=17.5-20.40.58=-5 Step 6 People from England are less than -5 which is the rejection region b. Some words on the GNT are more commonly used in England. For Example, a mitre, the headpiece worn by bishops, is worn by the archbishop of Canterbury in public ceremonies in England. No Canadian participant correctly responded to this item, whereas 55% of English adults correctly responded. Explain why we should be cautious about applying norms to people different from those on whom the test was normed. The differences in culture impact the results to the question being asked. Not everything is the same from one country to the next. c. When we conduct a one-tailed test instead of a two-tailed test, there are small changes in steps 2 and 4 of hypothesis testing. Conduct steps 2, 4, and 6 of hypothesis testing for a one-tailed test. -Null: H0:1=17.5 -Research: H0: 117.5 -Critical value: +1.65 - 60-17.50.58=73.28 -null is rejected, Canada is less than critical value d. Under which circumstance- a one-tailed or a two-tailed test- is it easier to reject the null hypothesis? Explain. One-tailed is easier to reject because you test for greater or less mean not both e. If it becomes easier to reject the null hypothesis under one type of test, does this mean that there is a bigger difference between the groups with a one-tailed test than with a two-tailed test? Explain. No, it does not mean a bigger difference 8.12- How are statistical power and effect size different but related? Power is the ability to find whether there is an effect and effect size is the size of the effect. If the power is greater than the effect size will also be greater. 8.46- Cheating with hypothesis testing: Unsavory researchers know that one can cheat with hypothesis testing. That is, they know that a researcher can stack the deck in his or her favor, making it easier to reject the null hypothesis. a. If you wanted to make it easier to reject the null hypothesis, what are three specific things you could do? - higher level, greater change of rejecting the null hypothesis - p-value for one-sided will be ½ as a two-sided test - the larger the sample, the increase in the probability b. Would it change the actual difference between the samples? Why is this a potential problem with hypothesis testing? Changing some situations but the group difference remains the same; The same mean difference is significant in some situations but not others