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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?A sample of five measurements, randomly selected from a normally distributed population. resulted in the following summary statistics: $ - 48,8 - 1.3, a. Test the null hypothesis that the mean of the population is 6 against the alternative hypothesis, P 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.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?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.Cooling method for gas turbines. During periods of high demand for electricity-especially in the hot summer months-the power output from a gas turbine engine can drop dramatically. One way to counter this drop in power is by cooling the inlet air to the turbine. An increasingly popular cooling method uses high-pressure inlet fogging. The performance of a sample of 87 gas turbines augmented with high-pressure inlet fogging was investigated in the Joumal of Engineering for Gas Turbines and Power (Jan. 2005). One measure of performance is heat rate (kilojoules per kilowatt per hour). Heat rates for the 67 gas turbines, saved in the GASTURBINE file, are listed in the next table. Suppose that a standard gas turbine has, on average, a heat rate of 10,000 kJ/kWh. a. Conduct a test to determine whether the mean heat rate of gas turbines augmented with high- pressure inlet fogging exceeds 10,000 kJ/kWh. Use a =_05. b. Identify a Type I error for this study. Identify a Type II error. 14822 13198 11948 11289 11964 10526 10387 10592 10480 | 10088 14828 13398 11726 11252 12449 11030 10787 10603 10144 11874 11510 10946 10508 10604 10270 |10529 10380 14796 12913 12270 11842 10656 11380 11136 10814 13523 11289 11183 10951 8722 10481 9812 9569 9643 9115 9115 11588 10888 9738 9295 9421 9105 10233 10186 9018 |9209 9532 9933 9152 9295 16243 14628 12786 8714 9469 11948 12414