In a poll of 516 human resource professionals, 45.7% said that body piercings and tattoos were big personal grooming red flags. Complete parts (a) through (c) below. a. Among the 516 human resource professionals who were surveyed, how many of them said that body piercings and tattoos were big personal grooming red flags? 236 (Round to the nearest integer as needed.) b. Construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big personal grooming red flags. 0.401

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In a poll of 516 human resource professionals,  45.7% said that body piercings and tattoos were big personal grooming red flags. Complete parts (a) through (c) below. a. Among the 516 human resource professionals who were surveyed, how many of them said that body piercings and tattoos were big personal grooming red flags? 236 (Round to the nearest integer as needed.) b. Construct a  99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big personal grooming red flags.  0.401 < p < 0.514 (Round to three decimal places as needed.) c. Repeat part (b) using a confidênce level of  80%.  < p < ◻ (Round to three decimal places as needed.)

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Calculate Number: a. Calculate the number of human resource professionals who said that body piercings and tattoos were big personal grooming red flags. Given that 45.7% of the 516 surveyed professionals believe that body piercings and tattoos are red flags, we multiply 0.457 by 516 to find the number. 0.457 * 516 = 235.812 We round to the nearest integer.Construct Confidence Interval: b. Construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big personal grooming red flags. We use the formula for the confidence interval for a proportion: CI = p̂ ± Z * sqrt[(p̂(1 - p̂)) / n] where p̂ is the sample proportion, Z is the Z-score corresponding to the confidence level, and n is the sample size. First, we find the Z-score for a 99% confidence level, which is approximately 2.576. Next, we calculate the standard error (SE): SE = sqrt[(0.457 * (1 - 0.457)) / 516] SE = sqrt[(0.457 * 0.543) / 516] SE = sqrt[0.248031 / 516] SE = sqrt[0.00048054] SE ≈ 0.0219 Now we calculate the margin of error (ME): ME = Z * SE ME = 2.576 * 0.0219 ME ≈ 0.0564 Finally, we construct the confidence interval: Lower bound = p̂ - ME Lower bound = 0.457 - 0.0564 Lower bound ≈ 0.4006 Upper bound = p̂ + ME Upper bound = 0.457 + 0.0564 Upper bound ≈ 0.5134 We round to three decimal places.Repeat for 80% Confidence: c. Repeat part (b) using a confidence level of 80%. For an 80% confidence level, the Z-score is approximately 1.282. We use the same standard error (SE) calculated in part (b). Now we calculate the margin of error (ME) for the 80% confidence level: ME = Z * SE ME = 1.282 * 0.0219 ME ≈ 0.0281 Construct the confidence interval: Lower bound = p̂ - ME Lower bound = 0.457 - 0.0281 Lower bound ≈ 0.4289 Upper bound = p̂ + ME Upper bound = 0.457 + 0.0281 Upper bound ≈ 0.4851 We round to three decimal places.

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