Can someone please help explain how to solve these problems? Thank you!

For this problem, carry at least four digits after the decimal In your calculations. Answers may vary slightly due to rounding. In a random sample of 62 professional actors, it was found that 43 were extroverts. (a) Letp 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 forp. (Round your answers to two decimal places.) lower Ilm it u pper limit Give a brief interpretation ofthe meaning of the confidence interval you have found. We are 5% confident that the true proportion of actors who are extroverts falls within this interval. A I A I I \\_1 We are 5% confident that the true proportion of actors who are extroverts falls above this interval. A I\\ II We are 95% confident that the true proportion of actors who are extroverts falls outside this interval. A We are 95% confident that the true proportion of actors who are extroverts falls within this interval. (c) Do you think the conditions my .2 5 and no :- 5 are satisfied in this problem? Explain why this would be an important consideration. "' Yes, the conditions are satised. This is important because it allows us to say that [3 is approximately normal. A I I \\_J No, the conditions are not satisfied. This is important because it allows us to say that .6 is approximately binomial. A I\\ ll Yes, the conditions are satised. This is important because it allows us to say that :3 is approximately binomial. A No, the conditions are not satisfied. This is important because it allows us to say that ,6 is approximately normal. For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations at a certain monument. At one excavation site a sample of 606 potsherds was found, of which 360 were identified as Santa Fe black-on-white. (a) Let p represent the proportion of Santa Fe black-on-white potsherds at the excavation site. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 95% confidence interval for p. (Round your answers to three decimal places.) lower limit upper limit Give a brief statement of the meaning of the confidence interval. O 95% of all confidence intervals would include the true proportion of potsherds. 5% of all confidence intervals would include the true proportion of potsherds. O 95% of the confidence intervals created using this method would include the true proportion of potsherds. O 5% of the confidence intervals created using this method would include the true proportion of potsherds. (c) Do you think that mp > 5 and nq > 5 are satisfied for this problem? Explain why this would be an important consideration. O Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately binomial. O No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial. Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal. O No, the conditions are not satisfied. This is important because it allows us to say that p is approximately normal.For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a marketing survey, a random sample of 736 women shoppers revealed that 640 remained loyal to their favorite supermarket during the past year (i.e., did not switch stores). (a) Let p represent the proportion of all women shoppers who remain loyal to their favorite supermarket. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 95% confidence interval for p. (Round your answers to three decimal places.) lower limit upper limit Give a brief explanation of the meaning of the interval. O) 95% of the confidence intervals created using this method would include the true proportion of loyal women shoppers. 5% of the confidence intervals created using this method would include the true proportion of loyal women shoppers. 5% of all confidence intervals would include the true proportion of loyal women shoppers. O 95% of all confidence intervals would include the true proportion of loyal women shoppers. (c) As a news writer, how would you report the survey results regarding the percentage of women supermarket shoppers who remained loyal to their favorite supermarket during the past year? O Report the confidence interval. O Report p along with the margin of error. Report p. O Report the margin of error. What is the margin of error based on a 95% confidence interval? (Round your answer to three decimal places.)For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. How hard is it to reach a businessperson by phone? Let p be the proportion of calls to businesspeople for which the caller reaches the person being called on the first try. (a) If you have no preliminary estimate for p, how many business phone calls should you include in a random sample to be 80% sure that the point estimate p will be within a distance of 0.04 from p? (Round your answer up to the nearest whole number.) phone calls (b) A report states that businesspeople can be reached by a single phone call approximately 22% of the time. Using this (national) estimate for p, answer part (a). (Round your answer up to the nearest whole number.) phone callsDo you want to own your own candy store? Wowl With some Interest In running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population ofx values has an approximately normal distribution. 96 1?5 135 94 3'5 94 116 100 85 (a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost; and sample standard deviation 5. (Round your answers to one decimal place.) ; = thousand dollars 5 = thousand dollars (b) Find a 90% confidence interval for the population average startup costs p for candy store franchises. (Round your answers to one decimal place.) lower limit thousand dollars upper limit thousand dollars