If your \(x = 542\) (ie the number of “successes” and your \(n = 3611\), this is how you can have R calculate a 90% Confidence Interval for you.

binom.test(x = 542, n = 3611,  conf.level = .90)[["conf.int"]]
## [1] 0.1403939 0.1602214
## attr(,"conf.level")
## [1] 0.9

25.

  1. p^=417/2306 =0.181
  2. np(1-p)=2306x0.181(1-0.181)=341.84???10 The sample is lees than 0.05 of the population
  3. Lower bound: 0.0181-1.64x Square root 0.181x0.819/2306=0.168 Upper bound: 0.181+1.64x Square root 0.181x 0.819/2306=0.194
  4. We are 90% confident that the population proportion if adult Americans 18 years old who have donated blood in the past two years is between 0168 and 0.194. s

26.

(a)p^=496/1153 =0.43 (b) np(1-p)=1153x0.43(1.0.43)=282.6???10 The samole is less than 0.05 of the populaiton (c) Lower bound: 0.43-1.96x Square root 0.43x0.57/1153=0.40 Upper bound: 0.43+1.96x Square root 0.43x0.57/1153=0.46 (d) We are 95% cinfident that the population proportion of workers and retires in the USA 25 years of age and older who have less than $10,000 in savings is between 0.40 and 0.46.

27.

  1. p^=521/1003 =0.519
  2. np(1-p)=1003x0.519(1-0.519)=250.39???10 The sample is less than 0.05 of the population
  3. Lower bound: 0.519-1.96x Square root of 0.519x0.481/1003=0.488 Upper bound: 0.519+1.96x Square root of 0.519x0.481/1003=0.550
  4. It is both possible and impossible. It is possible that the population proportion is more than 60%, because it is possible that the true proportion is not concluded in the confidence interval.But somwhow, it is not possible because 0.6 is outside of the confidence level.
  5. lower bound: 1-0.550=0.450 Upper bound: 1-0.488=0.512

28.

  1. p^=768/1024=0.75
  2. np(1-p)=1024x0.75(1-0.75)=192???10 The sample is less than 0.05 of the population
  3. lower bound:0.75-2.57x Square root of 0.75x0.25/1024=0.715 Upper bound: 0.75+2.57x Square root of 0.75x0.25/1024=0.785
  4. It is possible that the proportion of family values is extremely or very important in determining their vote for president is below 70%, because some may not include into the proportion, but it is not likely because 0.70 is outside of the confidence level.
  5. lower bound: 1-0.785=0.215 upper bound:1-0.715=0.285

29.

  1. p^=26/234=0.111 lower bound: 0.111-1.96x Square root of 0.111x0.889/234=0.071 upper bound:0.111+1.96x Square root of 0.111x0.889/234=0.151

  2. lower bound: 0.111-2.575x Square root of 0.111x0.889/234=0.058 upper bound: 0.111+2.575x Squae root of 0.111x0.889/234=0.164

  3. it will increase the margin of error.