Statistics questions:-
Emotional empathy in young adults. According to a theory in psychology, young female adults show more emotional empathy towards others than do males. The Journal of Moral Education (June 2010) tested this theory by examining the attitudes of a sample of 30 female college students. Each student completed the Ethic of Care Interview, which consisted of a series of statements on empathy attitudes. For the statement on emotional empathy (e.g.. "I often have tender, concerned feelings for people less fortunate than me"), the sample mean response was 3.28. Assume the population standard deviation for females is .5. [ Note : Empathy scores ranged from 0 to 4. where 0 = "never" and 4 = "always"] Suppose it is known that male college students have an average emotional empathy score of p = 3 . a. Specify the null and alternative hypothesis for testing whether female college students score higher than 3.0 on the emotional empathy scale. b. Compute the test statistic. c. Find the observed significance level ( p -value) of the test. d. At a = .01 , what is the appropriate conclusion? e. How small of an o -value can you choose and still have sufficient evidence to reject the null hypothesis?Suppose you are interested in conducting the statistical test of HO: p = 200 against HO: p > 200. and you have decided to use the following decision rule: Reject HO if the sample mean of a random sample of 100 items is more than 215. Assume that the standard deviation of the population is 80. a. Express the decision rule in terms of z. b. Find a, the probability of making a Type I error, by using this decision rule.Radon exposure in Egyptian tombs, Refer to the Radiation Protection Dosimetry (Dec. 2010) study of radon exposure in Egyptian tombs. Exercise 7.39 (p. 334). The radon levels-measured in becquerels per cubic meter (Bqim )-in the inner chambers of a sam- ple of 12 tombs are listed in the table, For the safety of the guards and visitors, the Egypt Tourism Authority (ETA) will temporarily close the tombs if the true mean level of radon exposure in the tombs rises to 6.000 Bq/m'. Consequently, the ETA wants to conduct a test to deter- mine if the true mean level of radon exposure in the tombs is less than 6,000 Bq/m , using a Type I error probabil- ity of .10. A SAS analysis of the data is shown on p. 399. Specify all the elements of the test: Ho, He, test statistic, p-value, a, and your conclusion. 50 910 180 580 7800 4000 390 12100 3400 1310 11900 1100 SAS Output for Exercise 8.64 The TTEST Procedure Variable: RADON Mean Sid Day Sid Err Minimum Maximum 12 3642 5 4486.9 1295 3 50.0000 12100.0 Mean 95% CL Mean Std Dev 95% CL Std Dev 3642.5 -Infty 5960.6 1406.9 3170.5 7610.3 t Value Pre t 11 -1.82 0 0480Yield strength of steel connecting bars. To protect against earthquake damage, steel beams are typically fitted and connected with plastic hinges. However, these plastic hinges are prone to deformations and are difficult to inspect and repair. An alternative method of connecting steel beams-one that uses high-strength steel bars with clamps-was investigated in Engineering Structures (July 2013). Mathematical models for predicting the performance of these steel connecting bars assume the bars have a mean yield strength of 300 megapascals (MPa). To verify this assumption, the researchers conducted material property tests on the steel connecting bars. In a sample of three tests, the yield strengths were 354. 370, and 350 MPa. Do the data indicate that the true mean yield strength of the steel bars exceeds 300 MPa? Test using or - ,01.70Pitch memory of amusiacs. Amusis is a congenital disorder that adversely impacts one's perception of music. Refer to the Advances in Cognitive Psychology (Vol. 8. 2010) study of the pitch memory of individuals diagnosed with amusia, Exercise. Recall that each in a sample of 17 amusiacs listened to a series of tone pairs and was asked to determine if the tones were the same or different. In the first trial, the tones were separated by 1 second; in a second trial, the tones were separated by 5 seconds. The difference in accuracy scores for the two trials was determined for each amusiac (where the difference is the score on the first trial minus the score on the second trial. The mean score difference was .11 with a standard deviation of .19. a. In theory, the longer the delay between tones, the less likely one is to detect a difference between the tones. Consequently, the true mean score difference should exceed 0. Set up the null and alternative hypotheses for testing the theory. b. Carry out the test, part a, using a = .05 . Is there evidence to support the theory?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 ]).Speeding and young drivers. Psychologists conducted a survey of 258 student drivers and their attitudes toward speeding and reported the results in the British Journal of Educational Psychology (Vol. 80, 2010). One of the variables of interest was the response to the question, "Are you confident that you can resist your friends'persuasion to drive faster?" Each response was measured on a 7-point scale, from 1 = "definitely no" to 7 = "definitely yes." The data were collected 5 months after the students had attended a safe-driver presentation. The psychologists reported a sample mean response of 4.98 and a sample standard deviation of 1 62. Suppose it is known that the true mean response of students who do not attend a safe-driver presentation is # =47. 3. Set up the null and alternative hypotheses for testing whether the true mean student-driver response 5 months after a safe-driver presentation is larger than 4.7. b. Calculate the test statistic for the hypothesis test c. Find the rejection region for the hypothesis test, using a - 105. d. State the appropriate conclusion, in the words of the problem. e. Do the test results indicate that the safe-driver presentation was effective in helping students feel more confident that they can resist their friends' persuasion to drive faster? Explain. f. The distribution of response scores (on a 7-point scale) for all student drivers is unlikely to be normal. Does this impact the validity of the hypothesis test? Why or why not?Increasing hardness of polyester composites. Polyester resins reinforced with fiberglass are used to fabricate wall panels of restaurants. It is theorized that adding cement kiln dust (CKD) to the polyester composite will increase wall panel hardness. In a study published in Advances in Applied Physics (Vol. 2. 2014). hardness (joules per squared centimeters) was determined for three polyester composite mixtures that used a 40% CKD weight ratio. The hardness values were reported as 83. 84, and 79 jom Research has shown that the mean hardness value of polyester composite mixtures that use a 20% CKD weight ratio is p - 76j/em In your opinion. does using a 40% CKD weight ratio increase the mean hardness value of polyester composite mixtures? Support your answer statistically.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?Packaging of a children's health food. Junk foods (e.g.. potato chips) are typically packaged to appeal to children. Can similar packaging of a healthy food product influence children's desire to consume the product? This was the question of interest in an article published in the Journal of Consumer Behaviour (Vol. 10. 2011). A fictitious brand of a healthy food product-sliced apples -was packaged to appeal to children (a smiling cartoon apple on the front of the package). The researchers showed the packaging to a sample of 408 schoolchildren and asked each whether he or she was willing to eat the product. Willingness to eat was measured on a 5-point scale, with 1 = "not willing at all" and 5 = "very willing." The data are summarized as follows: T = 3.69, x = 2.44, Suppose the researchers know that the mean willingness to eat an actual brand of sliced apples (which is not packaged for children) is A - 3. a. Conduct a test to determine whether the true mean willingness to eat the brand of sliced apples packaged for children exceeds 3. Use a = (is to make your conclusion. b. The data (willingness to eat values) are not normally distributed. How does this affect (if at all) the validity of your conclusion in part a? Explain
