Question

13. John Brown is a statistically-minded young man who is also on a fairly tight budget. Before he invites a certain young lady out for dinner, he would like to have a good idea of the cost of a meal for two at the restaurant where he would like to take her. How many two-meal combinations should he check in order to be 96% confident that the average price in his sample will be within $1.55 of the actual average price for a meal for two? Past studies from similar restaurants show that the standard deviation for the price of a meal for two is about $3.64. X = 14. A curious mom wants to determine what proportion of babies in her town take their first steps before their first birthday. How many babies' parents should she ask in order for her to be 90% confident that the proportion in her sample will be within 5% of the true proportion for her town? X = a. Studies indicate that about 73% of babies take their first steps before age 1, so she can use this as a planning value. b. What if there is no planning value available?

Answer 1

Q14 A) Here, we are using 0.73 as a planning value Q13) How many two mean combination should he check for a dinner? Givena B) Here planning value is unknown so we consider 0.5 as aplanning value. Givens Givens p= 0.73 p= 0.5 d = 3.64 E= 1.55 cl96 = 96 E= 0.05 CI= 90 E = 0.05 CI= 90 ...Assuming nothing is known about sample proportion, P(hat) is considered as 0.5 At 96% confidence level = At 90 % confidence level = At 90 % confidence level = a = 1-9696 = 1-0.96 = 0.04 Therefore, a/2 = 0.02 & Za /2 = 2.05 a = 1-9096 = 1-0.9 = 0.1 Therefore, a/2 = 0.05 & Za /2 = 1.64 a = 1-9096 = 1-0.9 = 0.1 Therefore, a/2 = 0.05 & Za/2 = 1.64 Now, Sample size = Now, Sample size = n= (Z/E)^2*p*(1-P) = (1.64/0.05)^2*0.73*(1-0.73) = 212.05 = 212 ...round to nearest whole number ... rounding to next whole number n= (Zºo/E)^2 = (2.05*3.64/1.55)^2 = 23.18 ... rounding to nearest whole number. = 24 ...rounding to next whole number, Now, Sample size = n= (Z/E)^2*p*(1-P) (1.64/0.05)^2*0.5*(1-0.5) = 268.96 = 269 ...round to nearest whole number = 2 23 = 213

pls upvote...!!!