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For each of the following rejection regions, sketch the sampling distribution of f and indicate the ocation of the rejection region on your sketch: 3. f> 1.440. where of = 6 b. * 2.060, where of = 25The following sample of six measurements was randomly selected from a normally distributed population: 1, 3. -1, 5, 1, 2. a. Test the null hypothesis that the mean of the population is 3 against the alternative hypothesis J 1,000, based on a sample of 17 observations. The test results are f = 1.89, p- value = 038. a. What assumptions are necessary for the validity of this procedure? b. Interpret the results of the test. c. Suppose the alternative hypothesis had been the twotailed Harp # 1,000. If the f-statistic were unchanged, what would the p -value be for this test? Interpret the p -value for the two-tailed test. If the f-statistic were unchanged, what would the p -value be for this test? Interpret the p - value for the two-tailed test.Dental anxiety study. Refer to the BMC Oral Health (Vol. 9, 2009) study of adults who completed the Dental Anxiety Scale, presented in Exercise. Recall that scores range from 0 (no anxiety) to 25 (extreme anxiety). Summary statistics for the scores of 15 adults who completed the questionnaire are 7 = 10.7 and s = 3.6. Conduct a test of hypothesis to determine whether the mean Dental Anxiety Scale score for the population of college students differs from p = 11. Use a = .05.Free recall memory strategy. Psychologists who study memory often use a measure of free recall(e.g., the number of correctly recalled items in a list of to-be remembered items). The strategy used to memorize the list-for example, category clustering-is often just as important. Researchers at Central Michigan University developed an algorithm for computing measures of category clustering in Advances in Cognitive Psychology (Oct. 2012). One measure, called ratio of repetition, was recorded for a sample of 8 participants in a memory study. These ratios are listed in the table. Test the theory that the average ratio of repetition for all participants in a similar memory study differs from .5. Select an appropriate Type I error rate for your test. .25 .43 .57 .3.8 .47 30 Source. Senlova, 0., & Oiani, H. "Calcpary clustering calculator for face recall" Advances in Cognitive Paychelogy Vol B. Na. 4. Oct 2012 (Table ]).Suppose a random sample of 100 observations from a binomial population gives a value of p =.60 and you wish to test the null hypothesis that the population parameter p is equal to.75 against the alternative hypothesis that p is less than.75. a. Noting that p =.80, what does your intuition tell you? Does the value of p appear to contradict the null hypothesis? b. Use the large-sample z-test to test HO: p =.75 against the alternative hypothesis Ha: p<.75. use d=".05." how do the test results compare with your intuitive decision from part a c. find and interpret observed significance level of you conducted in b.suppose sample exercise has produced we wish to ho: p=".9" against alternative ha: a. calculate value z statistic for this test. b. note that numerator p0=".84" is same as considering why absolute larger than calculated complete using result. d. its value.a random observations selected binomial population unknown probability success p. computed equal to.> 65. Use a =.01. b. Test HD: p =.65 against Ha: p >.65. Use a =.10. c. Test HO: p =.90 against Ha: p #.90. Use a =.05. d. Form a 95% confidence interval for p. e. Form a 09% confidence interval for p.In which 50 consumers taste-tested a new snack food. The data are saved in the SNACK file. 3. Test HO: p =.5 against Ha: p >.5, where p is the proportion of customers who do not like the snack food. Use a =.10. b. Report the observed significance level of your test. A random sample of 50 consumers taste-tested a new snack food. Their responses were coded (0: do not like: 1: like: 2: indifferent). recorded and saved in the SNACK file as follows: 1 12 01 1 0 10 2 0 2 2 0 0 1 1 0 0 0 0 1 0 2 0 0 0 1 0 0 1 0 0 1 0 1 0 2 0 0 1 10 1 a. Use an 80%% confidence interval to estimate the proportion of consumers who like the snack food b. Provide a statistical interpretation for the confidence interval you constructed in part a.Gummy bears: red or yellow? Chance (Winter 2010) presented a lesson in hypothesis testing carried out by medical students in a biostatistics class. Students were blind-folded and then given a red-colored or yellow-colored gummy bear to chew. (Half the students were randomly assigned to receive the red gummy bear and half to receive the yellow bear. The students could not see what color gummy bear they were given.) After chewing, the students were asked to guess the color of the candy based on the flavor. Of the 121 students who participated in the study. 97 correctly identified the color of the gummy bear. a. If there is no relationship between color and gummy bear flavor, what proportion of the population of students will correctly identify the color? b. Specify the null and alternative hypothesis for testing whether color and flavor are related. c. Carry out the test and give the appropriate conclusion at a =.01. Use the p -value of the test to make your decision.Facial structure of CEOs. Refer to the Psychological Science (Vol. 22, 2011) study on using a chief executive officer's facial structure to predict a firm's financial performance, Exercise 7.21 (p. 325). Recall that the facial width-to-height ratio (WHR) for each in a sample of 55 CEOs at publicly traded Fortune 500 firms was determined. The sample resulted in * = 1.96 and: = .15.. An analyst wants to predict the financial performance of a Fortune 500 firm based on the value of the true mean facial WAR of CEOs. The analyst wants to use the value of A = 22 Do you recommend he use this value? Conduct a test of hypothesis for u to help you answer the question. Specify all the elements of the test: 1/). /7,, test statistic, p-value, aand your conclusion. (Reference Exercise 7.21) Facial structure of CEOs. In Psychological Science (Vol. 22, 2011), researchers reported that a chief executive officer's facial structure can be used to predict a firm's financial performance. The study involved measuring the facial width-to-height ratio (WHR) for each in a sample of 55 CEOs at publicly traded Fortune 500 firms. These WHR values (determined by computer analyzing a photo of the CEO's face) had a mean of Y= 1.06 and a standard deviation of s = .15. a. Find and interpret a 95% confidence interval for p. the mean facial WHR for all CEOs at publicly traded Fortune 500 firms h. The researchers found that CEOs with wider faces (relative to height) tended to be associated with firms that had greater financial performance. They based their inference on an equation that uses facial WHR to pre- did financial performance. Suppose an analyst wants to predict the financial performance of a Fortune 500 firm based on the value of the true mean facial WHR of CEO&. The analyst wants to use the value of a - 2.2. Do you recommend he use this value