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Hypothesis Testing Questions and Examples

1. For each of the following questions, write the hypotheses that would be tested and then determine which hypothesis test should be used. Select from the following four choices.

• 1 proportion Z test

• 2 proportion Z test

• 1 sample t test

• 2 independent samples t test When writing hypotheses, the editor will not give you a way of typing in ? if you type the word mu, it will change to ? when you submit your answers. If you type the letters ne, with a space before and after it, they will change to ? when you submit your answers. If you need subscripts, use upper case letters. Note: the first question is different than the one in the book because the question in the book could be interpreted several ways and the answer in the back of the book is not correct. 1a. Is there a reduction in the average number of mistakes novice musicians makes after a week of practicing a piece?

The samples are dependent, meaning that each musician's count of mistakes after practicing would be compared to their count before they practiced. Their initial count will be subtracted from their final count (F - I) H 0 : H 1 : Test: Select an answer 1b. Do a majority of people eat raw cookie dough? H 0 : H 1 : Test: Select an answer Note:

Question 1c has been changed from the book. 1c. Is the proportion of STEM students at the Fort Steilacoom Campus (F) different than at the Puyallup Campus (P)? H 0 : H 1 : Test: Select an answer 1d. Is the average income of a self-employed person (SE) greater than a person working for a large company (LC)? H 0 : H 1 : Test: Select an answer 1e. Do you average more than 7 hours of sleep a night? H 0 : H 1 : Test: Select an answer 1f. Is the proportion of students with student loans less than 0.60? H 0 : H 1 : Test: Select an answer 1g. In a long race, such as a marathon, there are advantages to negative splitting the race. That means that the second half of the race is faster than the first half. For elite marathoners, will the average difference (second half - first half) be less than 0? (For example, first half split: 1:06.44, second half split 1:06.01, so 1:06.01 - 1:06.44 = -0.43. The second half was faster than the first half. H 0 : H 1 : Test: Select an answer If some of your hypotheses are marked wrong, but you think they are correct, email me and I will check them. Variation in choice of subscripts can lead to incorrect grading. Question HelpQuestion 1: Forum Post to forum Submit QuestionQuestion 1 Unattempted

Question 2 Check 0/7 ptsRetries 8 Test the following hypotheses. Assume all assumptions for the tests have been met. Write an appropriate concluding sentence. 2. When a young adult leaves home and lives on their own for the first time, they become responsible for feeding themselves. In general, there are two options, eat out or cook for themselves. Suppose someone hypothesized that the average they spent on eating out, including tax and tip, is less than $18 per day. For 31 days, they keep all their receipts and find the mean amount spent per day is $17.9 with a standard deviation of $2.9. Test the hypothesis that the mean they spend per day is less than $18. ? = 0.1 Write the hypotheses: H 0 : H 1 : At the level of significance, the mean money spent per day Select an answer significantly less than 18 (t= , p Select an answer , n = ) Question HelpQuestion 2: Forum Post to forum Submit QuestionQuestion 2 Unattempted

Question 3 Check 0/8 ptsRetries 8 Test the following hypotheses. Assume all assumptions for the tests have been met. Write an appropriate concluding sentence. 3. When a child has been adopted, they may grow up wondering why their birth parents placed them up for adoption. When a child was place in a closed/sealed adoption, there were laws preventing the birth parent from finding the child, and the child from finding the birth parent. Technology and some changes in the laws now allow these children to find their birth parents. However, there is no guarantee the birth parent will be happy to be found.

The child runs an enormous risk of the birth parent declining to meet them. On the other hand, some birth parents are delighted to be found and fully appreciate the reunification. Test the hypothesis that the proportion of the reunions with a favorable outcome is greater than 0.5 if a survey of children who found their birth parents resulted in 73 out of 128 having a favorable result. Let ? = 0.05 For the hypotheses, write mu if you want ? and write ne with a space before and after it if you want ? . Write the hypotheses: H 0 : H 1 : What is the sample proportion, ˆ p ? At the level of significance, the proportion of reunions that are favorable Select an answer significantly greater than 0.5 (z= , p = , n = ) Question HelpQuestion 3: Forum Post to forum Submit QuestionQuestion 3 Unattempted

Question 4 Check 0/8 ptsRetries 8 4. US News and World Report has stated what many think, the cheapest time to buy airline tickets is on Tuesdays after 3 pm Eastern time. http://money.usnews.com/money/personal-finance/articles/2012/04/18/8-insider-secrets-to-booking-cheap-airfare viewed 4-30-17. Use the data in the table below to determine if the mean difference between the Tuesday price and the regular price is less than 0. Data was collected from Travelocity.com in May 2017 for round-trip flights on Sept 10-17 2017. Destination Airlines Day Regular Price Tuesday Price Tuesday Price minus Regular Price Seattle to Boston Alaska Sunday 420.40 420.40 0 Chicago to Dallas United Thursday 446.40 470.40 24 San Francisco to Orlando Delta Thursday 399.60 362.60 -37 Memphis to Phoenix American Saturday 277.90 277.90 0 Denver to Las Vegas Frontier Thursday 205.95 195.98 -9.97 New York to LA Jet Blue Saturday 411.40 411.40 0 Albuquerque to Philadelphia American Sunday 513.20 513.20 0 Test the hypothesis that the mean difference is less than $0.

Write the hypotheses: H 0 : H 1 : At the level of significance, the mean difference between other days and Tuesday is significantly less than 0 (t= , p Select an answer , n = ) What is the calculator p-value? Question HelpQuestion 4: Forum Post to forum Submit Question

Question 4 Unattempted Question 5 Check 0/9 ptsRetries 8 5. The concept of anchoring is one that makes us question our own rationality. An example of anchoring is when you see something you want to buy, but can't afford and are then told the item is on sale. Suddenly, it looks like a good price. On the other hand, if someone told you they had bought the same item for half the price you paid, you would feel cheated. Daniel Kahneman and Amos Tversky were researchers who investigated anchoring. This concept was tested in an experiment with the Spring 2017 statistics class.

The class was asked to write down the last two numbers of their phone number. If the last two numbers were less than or equal to 40, they were "Low" numbers. If the last two numbers were greater than or equal to 60, they were "High" numbers. Then they were asked to write down their guess for the population of Morocco. The objective is to determine if the people who wrote down high numbers had a higher average estimate of Morocco's population than those low numbers. Use a level of significance of 0.1. Use H for high numbers and L for low numbers. Last 2 digits of phone number n Mean Minimum Maximum Standard Deviation <=40 (L) 15 19.2 1 110 27.51 >=60 (H) 15 58.5 1.6 248 73.87 For hypotheses, type mu for ? and type ne with a space before and after it, for ? . Write the hypotheses: H 0 : H 1 : At the level of significance, the mean estimate of Morocco's population by students with a high number on their phone Select an answer significantly greater than than for students with a low number on their phone (t= , p Select an answer , n H = , n L = ) What is the calculator p-value? Question HelpQuestion 5: Forum Post to forum Submit Question

Question 5 Unattempted Question 6 Check 0/8 ptsRetries 8 6. Since more people are aware of the problem of waste and are attempting to do their own part in reducing wasted bags by bringing their own reusable bags to a grocery store or not using a bag at all, is it possible that the proportion of shoppers using bags provided by the grocery store is different than 0.45? Data: Out of 619 shoppers, 243 used a paper bag provided by the store (plastic bags are illegal in Seattle where this study by statistics students was conducted). Let ? = 0.05 For the hypotheses, write mu if you want ? and write ne without a space before or after it if you want ? . Write the hypotheses: H 0 : H 1 : What is the sample proportion, ˆ p ? At the level of significance, the proportion of reunions that are favorable Select an answer significantly different than 0.45 (z= , p = , n = ) Question HelpQuestion 6: Forum Post to forum Submit Question

Question 6 Unattempted Question 7 Check 0/8 ptsRetries 8 7. The Tacoma-Pierce County Health Department conducts a Healthy Youth Survey to assess the health-related behaviors of Pierce County. The survey is given to students in grades 6,8,10 and 12. The data from the 2002 and 2012 reports will be used to determine if the proportion who use marijuana or hashish in 2012 is different than the proportion who used it in 2002. Use a 0.05 level of significance. 7a. Write the hypotheses that will be tested. For notation purposes, use a subscript A for 2012 and B for 2002. Type mu for ? and type ne with a space before and after it, for ? .

Write the hypotheses: H 0 : H 1 : A: 2012 B: 2002 x 172 526 n 653 2146 7b. Find the sample proportion for each year. 2012 2002 7c. What is the z value? What is the p-value? 7d. Write a concluding sentence as you've been taught. 7e. Washington legalized recreational use of marijuana for adults in 2012. Do you expect the use of marijuana by 12th graders to increase, remain the same, or decrease because of this new law? Why? Question HelpQuestion 7: Forum Post to forum Submit Question

Question 7 Unattempted Question 8 Check 0/25 ptsRetries 8 Briefing 5.2: Trailblazing Women In 1966, Bobbi Gibb applied to participate in the Boston Marathon. The director wrote her back saying "women are not physiologically able to run marathon distances, and we wouldn't want to take the medical liability. " That was during a time when opportunities were limited for women because of the assumption they were physically incapable of doing many of the things that men could do. The brief story is that Bobbi crashed the race wearing her brother's shorts and a sweatshirt, but within 30 seconds, some of the men realized she was a woman and where glad she was in the race. Spectators realized it too. "As Gibb ran by the crowds, she saw their reactions.

Men were cheering and clapping, and women were jumping wildly up and down and weeping." She finished ahead of two thirds of the other runners. Six years later, the rules were changed to allow women to run in the Boston Marathon. Now that women are allowed to compete on an equal basis with men, we can explore the differences in performance in longer athletic events. One of the most grueling competitions is the Ironman Triathlon in which participants swim 2.4 miles, bicycle 112 miles and then run a full 26.2-mile marathon. Results from the 2013 Canadian Ironman Triathlon in Whistler, BC will be used to compare the times of the non-professional participants.

The question is whether the mean time for men is less than the mean times of women. Use a 0.05 level of significance. 8a. Complete the design layout table. Research Design Table Research Question Grouping/explanatory Variables (if present) Levels (column headings or subscripts) Response Variable What type of data categorical quantitative What is the parameter that will be calculated correlation mean proportion List potential confounding variables Men 16 13.8 12.5 10.2 12.2 9.8 15.4 11.6 Women 10.9 12.9 13.2 14.7 13 12.1 13.9 15 16 15.4 8b. Write the hypotheses: Use subscripts of M and W. Use mu for ? and ne for ? . Hypothesis: Is the mean time men less than the mean time for women? H 0 : H 1 : 8c. Upload a side-by-side box plot here. No file chosen

Question 8 Part 12 of 25Choose FileNo file chosen 8d. Find the mean and standard deviation for the men and women. n mean standard deviation men women 8e. Test the hypotheses (you may use your calculator, you don't need to write the formula). Test Statistic t = p-value = 8f. Complete the concluding sentence. At the 0.05 level of significance, the mean time for men Select an answer significantly less than women (t = , p = , n M = , n W = ). Question HelpQuestion 8: Forum Post to forum Submit Question

Question 8 Unattempted Question 9 Check 0/23 ptsRetries 8 9. Why Statistical Reasoning is Important for Psychology Students and Professionals In collaboration with Tom Link, Professor of Psychology Based on the research article "How Does Stigma "Get Under the Skin"?" by Mark Hatzenbuehler, Susan Nolen-Hoeksema, and John Dovidio, published in the Jorunal of the Association for Psychological Science in 2009. This topic is taught in Psyc 100 (General Psychology) and Psyc 210 (Social Psychology) What strategies are most effective for avoiding adverse mental health issues for victims of discrimination? Briefing 6.3. Various groups of people feel stigma-related stress. The concept of social stigma was originally discussed by psychologist Erving Goffman in the 1963 publication Stigma:

Notes on the Management of Spoiled Identity. Stigma is defined as "a set of negative and often unfair beliefs that a society or group of people have about something". These groups include African Americans, LGB (lesbian, gay, bisexual), women, criminals, and obese individuals. There is some research that links stigma-related stressors to adverse mental and behavioral health. Stigma can be concealed for LGB individuals or criminals but not for the other groups. This means that people cannot tell if another person is gay unless they have been told, so the stigma is concealed from them (also called discreditable stigma). In contrast, skin color or gender is evident to another person instantly (also called discredited stigma). Individuals subjected to discrimination have a variety of ways to respond. Two of the ways include rumination and distraction.

Rumination is the process of focusing on yourself and reflecting on why you received such treatment. Distraction is to have your thoughts focused on something other than how you feel and the discrimination situation. Psychological distress, the dependent variable, will be used as a measure of mental health. It will be measured with a commonly used test. There are three questions that will be asked in this problem. To answer these three questions, the researchers used undergraduate students and community members. The data to answer the first question will come from a daily diary the subjects maintain. The data for the second question will come from surveys given to the subjects after they wrote about a time when they were victims of discrimination.

The data for the third question will be based on another survey the subjects take after they are directed towards one of the two coping mechanisms, rumination or distraction, using a random process (e.g. coin flip). You may use your calculator to test these hypotheses. You do not need to write the formulas or show substitution. For writing hypotheses, type mu for ? and ne for ? . 9a. Is the proportion of days with a discriminatory incident greater than for African Americans than it is for LGB individuals? ? = 0.05 African American and LGB subjects recorded stigma-related stressors in a journal. number of participants Days with at least one stigma-related stressor (x) Number of days of data (n) African Americans 18 140 191 LGB 31 225 311 Use subscripts A for African Americans and L for LGB

Write the hypotheses: H 0 : H 1 : What is the sample proportion for African Americans, ˆ p A ? What is the sample proportion for LGB, ˆ p L ? At the 0.05 level of significance, the proportion of of days with a stigma related event for African Americans Select an answer significantly greater than than for LGB (z= , p = , n A = , n L = ) 9b. Is the mean psychological distress score of African Americans different than LGB individuals following an experiment in which the individual had to recall a discrimination issue they faced? ? = 0.05 n Average Psychological Distress Standard Deviation African Americans 18 4.69 3.96 LGB 31 4.49 4.53 Use subscripts A for African Americans and L for LGB Write the hypotheses: H 0 : H 1 : At the 0.05 level of significance, is the average psychological distress score for African Americans Select an answer significantly different than than for LGB (t= , p = , n A = , n L = ) 9c. Is the the mean psychological distress score of those who used rumination to cope with the discrimination different than those who used distraction? n Mean Standard Deviation Rumination 25 13.25 6.21 Distraction 28 9.86 4.2 Use subscripts R for rumination and D for distraction Write the hypotheses: H 0 : H 1 : At the 0.05 level of significance, the mean psychological distress score of those who used rumination to cope with discrimination Select an answer significantly different than than for those using distraction (t= , p = , n A = , n L = ) Question HelpQuestion 9: Forum Post to forum Submit QuestionQuestion 9