Concussions among school aged children is a leading concern for parents througho

Question

Concussions among school aged children is a leading concern for parents throughout the US, and parents want to know the proportion of all children that have suffered a concussion at one point or another. In a random sample of 300 children, 48 had suffered from a concussion. Use this information to answer the next 4 questions. 17. If you wanted to calculate a 92% confidence interval for the proportion of all school age children whom have suffered a concussion (p), the value of Z" would be which one of the following? a. 0.516 b. 0.04 C. 141 d. 1.75 18. Calculate a 95% confidence interval for the proportion of all school age children whom have suffered a concussion (p). a. b, c. d, 0.16±0.0211 0.48 ±0.0565 0.16 ± 0.0565 0.16±0.0415 19. Which of the following statements would be a correct interpretation of the confidence interval calculated in the above question? We are 95% confident that the number of children whom have suffered a concussion is 48. a. b. We are 95% confident that the population proportion (p ) of children whom have C. We are 95% confident that the sample proportion (p ) of children who have suffered a d. We are 95% confident that the sample size is 300 children. suffered a concussion is captured by the interval above. concussion is 16%. 20. If the confidence level were to increase, from 95% to 98% confidence, while everything else remained the same, what would be the impact to the confidence interval? a. b. c. d. Become wider (or bigger) Become more narrow (or.smaller) Stay the same Determining the impact of confidence on the confidence interval is not possible with the information provided

Explanation / Answer

17)for 92% confidence interval; critical z =1.75

option D

18)

here estimated proportion phat =48/300 =0.16

for n=300 ; std error =(phat*(1-phat)/n)1/2 =0.0212

for 95% CI ; crtiical z =1.96

therrefore 95% CI =sample mean -/+ z*Std error =0.16+/-0.0415

option D

19)

option B is correct

19)option A is correct

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