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You are conducting a hypothesis test at the .03 level of significance, and you have computed a pvalue of .0478. What is your conclusion – do you reject the null hypothesis or do you fail to reject the null hypothesis? Explain your answer. 2. A social scientist wants to determine whether the marital status (divorced or not divorced) of U.S. men is independent of their religious affiliation (or lack thereof). A sample of 500 U.S. men is surveyed and the results tabulated below (here, A, B, C and D represent religions): A B C D None Total Divorced 39 19 12 28 18 116 Never Divorced 172 61 44 70 37 384 Total 211 80 56 98 55 500 At the α = .01 of significance, test to see whether there is sufficient evidence to indicate that the marital status of men who have been or are currently married is dependent on religious affiliation. 3. The city of Danville has had two major concerts: one (held by Phineas and Ferb) was to promote awareness of the aglet (the little plastic thing at the end of shoelaces), and the second was given by 80s icon Lindonna and 80s has-been Max Modem. The following people attended both concerts, with the amount spent on their tickets given in the table. Person 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Aglet concert 20 20 20 25 25 22 24 25 20 15 15 15 10 15 Lindonna concert 30 31 25 32 34 24 25 25 22 30 27 28 13 21 At the .05 level of significance, is there evidence to show that people spent more at the Lindonna concert than the Aglet concert? You may assume whatever is necessary regarding the distribution of the data set to answer this question. 4. Being nice brothers, Phineas and Ferb built their sister, Candace, a new phone to replace her old broken phone. This new phone contained 164 apps (including a rim-shot app). However, is this an unusually high number of apps for a teenage girl? Phineas and Ferb take a random sample of teenage girls and determines the number of apps they have on their phone, given below. 142, 157, 168, 101, 112, 125, 137, 140, 122, 111, 114, 128, 136, 126, 137 You may assume the data is normally distributed. At the .05 level of significance, is there evidence that Candace has an unusually high number of apps on her phone? 5. Recently, Sophia and Blanche were in competition to win the affection of a man, Fidel Santiago. Unfortunately, Fidel suffered a heart attack and passed away. This got Sophia and Blanche to wonder – were they the cause of Fidel’s heart attack? To address the question, they take a sample of 245 people who knew Fidel and asked if they believed the women caused the heart attack. Of those sampled, 156 agreed and said that Sophia and Blanche did cause the heart attack. At the .05 level of significance, is there evidence to show that a majority (more than 50%) think Sophia and Blanche caused the heart attack? 6. Dr. Heinz Doofenshmirtz is always having his “inators” blow up (such as the “go-away-inator”, the “ozone deplete-inator” and the “chicken-soup-inator”), mostly due to the influence of Perry the Platypus. He takes a random sample of 150 “inators” that he built, and found out that 92 of them have blown up. Construct a 98% confidence interval for the proportion of “inators” that have blown up. Based on your confidence interval, is there evidence that a majority of them (more than 50%) have blown up? 7. Interferons are proteins produced naturally by the human body that help fight infections and regulate the immune system. A drug developed from interferons, called Avonex, is now available for treating patients with multiple sclerosis (MS). In a clinical study, 85 MS patients received weekly injections of Avonex over a 2-year period. The number of exacerbations (i.e. flare-ups of symptoms) was recorded for each patient and is summarized in the next table. For MS patients who take a placebo (no drug), it is known from previous studies that 26% will experience no exacerbations, 30% one exacerbation, 11% two exacerbations, 14% three exacerbations and 19% four or more exacerbations. Number of Exacerbations Number of Patients 0 32 1 26 2 15 3 6 4 or more 6 Conduct a test to determine whether the exacerbation distribution of MS patients who take Avonex differs from the percentages reported for placebo patients. Test using α = .05. 8. Raj Koothrappalli is being constantly bombarded (by his parents) about the fact that he is over 30, and is still not married. He would like to claim that it is ok that he isn’t married yet, because men get married later than women, but he needs to find some evidence of this. As a result, he takes a random sample of married people and determines the age when they were married (and their gender), given below: Male: 27, 29, 31, 32, 30, 28, 22, 26, 27, 33, 37, 31, 28 Female:21, 23, 22, 29, 31, 27, 25, 25, 24, 22, 30, 19 You may assume both sets of data are normally distributed. At the .05 level of significance, is there evidence (from Raj’s data) that the average age of men is higher than the average age of women when they get married? 9. In an attempt to move on from his ex-wife Dorothy, Stan has spent time with a psychiatrist, Dr. Halperin. Dr. Halperin’s main technique is “transference”, where he has his patients transfer their love of a person to a fake monkey (Stan’s monkey was named “Fifi”). However, the technique seems to fail on a regular basis. Is there a difference in the success rates for males and females? To test this thesis, Dr. Halperin takes a random sample of 125 males that have participated in this therapy and finds that 82 of them did not have success with this therapy. Additionally, Dr. Halperin takes a random sample of 140 females that have participated in this therapy and finds that 62 of them did not have success with this therapy. At the .05 level of significance, is there evidence to show that males are less successful with this therapy than females? 10. Recently, Raj’s sister came to town and ended up dating his friend, Leonard. This led to a huge fight about one of the great questions of all time: is it ok to date the sibling of your friend? To determine if there is a difference in opinion among men and women, two simple random samples were taken. Of 136 men asked, 15 said it was ok for a friend to date their sibling. Of 127 women asked, 29 said it was ok for a friend to date their sibling. (a) Construct a 95% confidence interval for the difference in the proportion of men that say it is ok for a friend to date their sibling and the proportion of women that say it is ok for a friend to date their sibling. (b) Based on your answer to (a), is there evidence to show that women are more likely to “allow” their friend to date their sibling? 11. While Buford is best known for being a bully and Baljeet is best known for being a nerd, the two friends claim to spend lots of time studying. Two independent samples of recent tests taken by the two boys were gathered, and the amount of time studying for these tests recorded. Buford: 50, 20, 45, 35, 40, 15, 55, 20, 30, 40, 25 Baljeet: 70, 45, 40, 55, 50, 20, 55, 35, 60, 45, 65, 80, 85 You may assume that both sets of data are normally distributed. (a) Construct a 95% confidence interval for the difference in time spent studying on their exams. (b) Is there evidence to suggest that one of them spends more time studying than the other? If so, which one? Explain. 12. Create an example where someone would be interested in a confidence interval for matched pairs. You do not need to collect any data, and you do not need to find a confidence interval. Just give a scenario where someone would want such an interval. 13. You are going to conduct a goodness of fit test for a sample set of data. There are 112 data points that will be split up into 7 categories. If the test is at the .01 level of significance, what is the critical value of chi-square? 14. On the calculator, within 2SampTTest (and also within 2SampTInt), there is a place that says “Pooled: No Yes”. When would we want YES to be darkened? When would we want NO to be darkened? Is there a difference? Does it even matter? Explain your thoughts. 15. Sheldon Cooper is fluent in Klingon (including knowing how to say “Revenge is a dish best served cold” to Wil Wheaton). It got him to think about how many people are fluent in the language. If Sheldon would like to construct a 95% confidence interval for the proportion of people that are fluent, and would like his interval to be no more than 10 percentage points in width, how large a sample should he take? 16. After being elected presiding officer of the Faculty Senate in 2011, Professor Simpson thought about how the Senate meetings will go during his first year at the helm. Consider the following hypotheses: H0: Professor Sonia will run effective meetings this year (2011). H1: Professor Sonia will not run effective meetings this year (2011). If Professor Sonia performs a hypothesis test here and makes a Type I error, what would Professor believe is the truth? What would be the actual truth?

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1. We know that the acceptance and the rejection of the null hypothesis is based on the value of level of significance i.e. if the p-value is less than the level of significance then we will reject the null hypothesis otherwise we will accept the null hypothesis. Since the level of significance is 0.03 and the p-value is 0.0478, therefore, we are fail to reject the null hypothesis.

2. The hypothesis is:
Null Hypothesis:
H0: There is no statistically significant evidence to indicate that the marital status of men who have been or are currently married is dependent on religious affiliation.
Alternative Hypothesis:
HA: There is a statistically significant evidence to indicate that the marital status of men who have been or are currently married is dependent on religious affiliation.
The test statistic is:
χ2 = ∑(O-E)²/E
We know that the expected value is being calculated as
Ei = (ith Column Total/N)*ith Row Total...

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