Based on the information given for each of the following studies, decide whether to reject the null hypothesis. For each, give (a) the Z-score cutoff (or cutoffs) on the comparison distribution at which the null hypothesis should be rejected, (b) the Z score on the comparison distribution for the sample score, and (c) your conclusion. Assume that all populations are normally distributed
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Based on the information given for each of the following studies, decide whether to reject the null hypothesis. For each, give
(a) the Z-score cutoff (or cutoffs) on the comparison distribution at which the null hypothesis should be rejected,
(b) the Z score on the comparison distribution for the sample score, and
(c) your conclusion. Assume that all populations are
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- A random sample of 415 potential voters was interviewed 3 weeks before the start of a state-wide campaign for governor; 223 of the 415 said they favored the new candidate over the incumbent. However, the new candidate made several unfortunate remarks one week before the election. Subsequently, a new random sample of 630 potential voters showed that 317 voters favored the new candidate. Do these data support the conclusion that there was a decrease in voter support for the new candidate after the unfortunate remarks were made? Give appropriate statistical evidence to support your answer.Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance. Misleading Survey Responses In one presidential election, voting records showed that 61% of eligible voters actually did vote. In a survey of 1002 people, 70% said that they voted in that election (based on data from ICR Research Group). If survey respondents answered honestly and with accurate recall, there is about a 0.0000006% chance of getting such results.1. Peripheral catheters retained in a blood vessel are a common cause of peripheral vascular catheter-related bloodstream infections (PVC-BSIs) (Sato et al. 2017). Patients with PVC-BSIs appear to also have other infections such as Staphylococcus aureus (S. aureus). Researchers want to know if having an S. aureus infection is associated with dying from a PVC-BSI. In a recent trial, 187 patients were studied. 76 patients that had an S. aureus infection also died of a PVC-BSI. 35 patients died of a PVC-BSI but did not have an S. aureus infection. 22 patients had an S. Aureus infection but did not die of a PVC-BSI. Finally, 54 patients did not have an S. aureus infection and did not die of a PVC-BSI. Test the claim that PVC-BSI mortality is dependent upon having an S. aureus infection. Use a 0.05 significance level. a. 0.31 b. 0.45 c. 3.94 d. 2.14 e. 4.54
- A researcher is interested in the average age people first develop symptoms of aparticular condition they are investigating. They record the ages of first developingsymptoms from 30 random people (below) who have been involved in a recentlarge trial on managing the condition. 25, 19, 60, 76, 52, 42, 56, 99, 61, 42, 70, 23, 23, 19, 18, 54, 72, 18,42, 33, 42, 19, 41, 24, 67, 70, 23, 21, 30, 22 i. Calculate a 95% and 99% confidence interval for the average age of firstdeveloping symptoms. Carefully explain the two confidence intervalsand why they differ. ii. Previous well-established research shows that the average age of firstdeveloping symptoms was around 30. Are your findings consistent withthis? iii. We are interested in independent and identically distributed (iid)random variables when sampling. What do you understand by an iidand do you think the survey data in this case is iid? iv. A colleague has asked for a smaller confidence interval. How might thisbe achieved?The Genetics and IVF Institute conducted a clinical trial of the YSORT method designed to increase the probability of conceiving a boy. As of this writing, 291 babies were born to parents using the YSORT method, and 239 of them were boys. Use significance level to test the claim that the YSORT method is effective in increasing the likelihood that a baby will be a boy. State the null and alternate hypotheses (write it mathematically) and write your claim. Find the test statistic Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using the critical value. Find the p-value and interpret its meaning. Decide whether to reject or fail to reject the null using the p-value approach.A researcher wishes to assess the possibility that a certain type of psychotherapy actually reduces neurotic symptoms. A random sample of subjects is selected from the population of names on a waiting list at a mental health clinic. For each subject selected, another subject is so, also from the waiting list, who resembles the original deselect exception in a number of important respects, such as age, length of time on the waiting list, IQ, severity of symptoms, length of symptoms duration, category of neurosis, and previous treatment history. By a flip of a coin, one group is chosen to receive six months of intensive Psychotherapy, while the other group is told to continued waiting and not to seek treatment elsewhere. At the end of the six-month period, a panel of expert judges all the subjects with respect to the extent of symptomatology. What type of research is this, experimental or post facto? What is the IV and what is the DV? What would you advise the researcher to do with…
- A recent study at a college classified a group of 200 students according to whether they attended their classes and whether they passed a particular exam. 93 students attended their classes and passed the exam, 7 students didn't attend their classes but passed the exam, and 60 students didn't attend their classes and failed in the exam. The researcher in the study computed the test statistics. What hypothesis can be tested using the test statistics above And Compute the test statistics appearing above and test the hypothesis of interest . Interpret theresults.A farming cooperative in Capetown buys wheat seeds for its farmer members from seed merchants. A particular seed merchant claims that their wheat seeds have at least an 80% germination rate. Before the farming cooperative will buy from this seed merchant, they want to verify this claim. A random sample of 320 wheat seeds supplied by this seed merchant was tested, and it was found that only 230 seeds germinated. Is there sufficient statistical evidence at the 3% significance level to justify the purchase of wheat seeds from this seed merchant? Use the p-value approach to conduct a hypothesis test for a single proportion, and report the findings to the Capetown farming cooperative.Erythropoietin (EPO) is a banned drug used by athletes to increase the oxygen-carrying capacity of their blood. New tests for EPO were first introduced prior to the 2000 Olympic Games held in Sydney, Australia. Chance (Spring 2004) reported that of a sample of 830 world-class athletes, 159 did not compete in the 1999 World Championships (a year prior to the new EPO test). Similarly, 133 of 825 potential athletes did not compete in the 2000 Olympic Games. Was the new test effective in deterring an athlete’s participation in the 2000 Olympics? If so, then the proportion of nonparticipating athletes in 2000 will be greater than the proportion of nonparticipating athletes in 1999. Use a 98% confidence interval to compare the two proportions and make the proper conclusion.
- An educational psychologist studies the effect of frequent testing on retention of class material. In one of the professor's sections, students are given quizzes each week. The second section receives only two tests during the semester. At the end of the semester, both sections receive the same final exam, and the scores are summarized below. Do the data indicate that testing frequency has a significant effect on performance? Use a two-tailed test with α = .01. Include the null hypothesis in symbols, critical region(s), and a conclusion about significance. Compute r2 and state the size of the effect (e.g. small, medium, large). Frequent Quizzes Two Exams n = 15 n = 15 M = 72 SS= 112 M = 68 SS= 983. Super Slim, a weight loss society, is offering a weight reduction programme that they advertise will result in a waist loss in the first 30 days of the programme. Twenty-six subjects were independently and randomly selected for a study, and their waist sizes before and after the weight loss programme were recorded. Test the hypothesis at a 0.05 significance level that the claim made by super slim is valid using the dataset “super_slim”. 3.1. Define the hypothesis. 3.2. Calculate the test statistic. 3.3. Provide a conclusion.data super_slim;input customer $ before after;datalines;1 199 1192 111.3 107.13 113.4 90.34 107.01 100.15 123.9 95.96 116.9 93.87 110.6 93.18 124.6 89.69 98.7 106.410 114.1 99.4 11 107.8 9812 111.3 107.813 111.3 100.114 96.6 102.915 112.7 99.416 109.2 104.317 115.5 95.218 110.6 107.819 105.7 9820 115.5 101.521 108.5 97.522 107.8 9823 102.9 87.524 109.2 98.725 108.5 102.226 118.3 94.5;run;The table below lists the frequency of wins for different post positions in a horse race. A post position of 1 is closest to the inside rail, so that horse has the shortest distance to run. (Because the number of horses varies from year to year, only the first 10 post positions are included.) Use a 0.05 significance level to test the claim that the likelihood of winning is the same for the different post positions. Based on the result, should bettors consider the post position of a horse race? Post Position 1 2 3 4 5 6 7 8 9 10 Wins 20 15 12 16 15 7 9 12 6 12 Determine the null and alternative hypotheses. H0: ▼ At least one post positions have a different frequency of wins than the others. Wins occur with equal frequency in the different post positions. Wins occur with all different frequency in the different post positions. At least one post position has a different frequency of wins than the others.…