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For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a Iandom sample of 66 professional actors, it was found that 39 were extroverts. Ia USES (a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.) :| (b) Find a 95% condence interval for ,0. (Round your answers to two decimal places.) Give a brief interpretation of the meaning of the condence interval you have found. 0 We are 95% oondent that the true proportion of actors who are extroverts falls within this interval. 0 We are 95% oondent that the true proportion of actors who are extroverts falls outside this interval. 0 We are 5% condent that the true proportion of actors who are extroverts falls above this interval. 0 We are 5% condent that the true proportion of actors who are extroverts falls within this interval. (c) Do you think the oonditions np > 5 and nq > 5 are satised in this problem? Explain why this would be an important consideration. 0 No, the oonditions are not satised. This is important because it allows us to say that p is approximately binomial. O No, the oonditions are not satised. This is important bemuse it allows us to say that .6 is approximately normal. 0 Yes, the conditions are satised. This is important because it allows us to say that is approximately normal. 0 Yes, the conditions are satised. This is important because it allows us to say that p is approximately binomial. A random sample of 25 values is drawn from a moundrshaped and symmetric distributlnn. The sample mean is 7 and the sample standard deviatinrl is 2. Use a level orsignicante or 0.05 to conduct a twortaiie test of the claim that the population mean is IQ USE SA (a) Is it appropriate to use a student's t distribution? Explain. 0 Yes, because the x distribution is moundrshaped and symmetric and o is unknown. 0 No, the x distribution is skewed left. 0 N0, the x distribution is skewed right. 0 No, the x distribution is not symmetric. 0 N0, :1 is known. How many degrees of freedom do we use" \\:| (b) what are the hypotheses? 0 HD: pi : 5.5; H1: p x 5.5 0 HD: pi 5.5; H1: pi = 0.5 O HE: pi : 6.5; H1: p > 6.5 O HE: pi : 6.5; H1: p 0.250 O 0.100 0.5 O H:p : 0.5; H1:p 0.100 O 0.050 a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value s a, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the 5% level of significance, the evidence is sufficient to conclude that the natural distribution of browse does not fit the feeding pattern. At the 5% level of significance, the evidence is insufficient to conclude that the natural distribution of browse does not fit the feeding pattern.The types of browse favored by deer are shown in the following table. Using binocuiars, volunteers observed the feeding habits of a random sample of 320 deer. Plant Compmition Observed Number of Deer Tune of Browse in StudyArea Feeding on This Plant Sage brush 32% 102 Rabbit brush 38.7% 126 Salt brush 12% 45 Service berry 9.3% 25 Other 8% 22 Use a 5% level of significance to test the ciaim that the natural distribution of browse ts the deer feeding pattern. (a) What is the ievel of signicance? E State the null and alternate hypotheses. O H0: The distributions are the same. H1: The distributions are different. 0 H0: The distributions are different. H1: The distributions are the same. 0 H0: The distributions are different. H1: The distributions are different. 0 H0: The distributions are the same. H1: The distributions are the same. (b) the value of the chiisquare statistic for the sampie. (Round the expected frequencies to at least three decimal places. Round the test stastic to three decimal places.) E Are ali the expected frequencies greater than 5? 0 Yes Ohio What sampling distribution will you use? 0 binomiai 0 normal 0 uniform O Student's t O chiisquare What are the degrees of freedom? E 19. [-14 Points] DETAILS BBBASICSTATB &2.016t5u Do you went to own your own candy store7 Wow' with some interest in running your own business and a decent credit rating, you can prooeoly get a bank loan on startup costs fur franchises such as Candy Express, The Fudge Company, Kermel Corn, end Rucky Mountain chocolate Factory startup costs (in thousands ordollars) for a random sample of candy stores are given below. Assume that the population Dfx values has an approximately normal dlstrlbutlun. 94 172 125 95 75 94 115 mu E5 USE SALT (a) Use a calculator With mean and sample standard deviation keys to nd the sample mean startup cost; and sample standard deviation s (Round youranswers to fuur decimal places.) x \\:|housand dollars 5 \\:|thousand dollars (o) Find a snowo condence interval for the population average startup costs p for candy store franchises (Round your answers to one decimal place.) lower limit \\:|thousand dollars upper \\:|thousand dollars Need Help? 20. [-14 Points] DETAILS BBBASICSTATE 82.018ch 5' what percentage of hospitals provide at least some charity care? Based on a random sample wf hospital reports from eastern states, the following information is obtained [units in percentage of hospitals providing at least some charity care): 571 555 527 553 59m 547 7a: 547 535 7E2 | USE SA Assume that the population ofxvalues has an approximately normal distrioution. (a) Use a calculator with mean and sample standard deviation keys to nd the sample mean percentage} and the sample standard deviation 5. (Round your answers to four decimal places.) xeSee (b) Find a gun/a condence interval Furthe population average p of the percentage of hospitals providing at least some charity care. (Round your answers to one decimal place.) ieweime :ee upper