Question

are 1. Confidence intervals can be constructed only under certain assumptions about the samples and population. For each Situation below, either (1) construct the confidence interval, or (ii) explain why you cannot (which assumption is missing) and (iii) what would a researcher need to change to be able to construct the confidence interval (a) Suppose SAT scores for a population of students is normally distributed. The SAT scores for 12 randomly selected 1130 1290 1010 1320 950 1250 1340 1100 1260 1180 Construct a 95% confidence interval for the population mean score . (b) Based on a random sample of 50 days, the mean closing price of stock was $218.08. If the standard deviation of the stock over all days is $10.27, construct a 90% confidence interval for the mean stock price. (c) An opinion pollster randomly selected 10 people and asked whether they approve of the Mayor's response to COVID- 19. Of the sample, 7 of the 10 approved of the response. Construct a 99% confidence interval for the proportion of the population that approved of the Mayor's actions. (d) Out of a random sample of 200 undergraduates, 45 said they did not plan to continue college next semester. Construct a 99% confidence interval for the percentage of undergraduates that do not plan to continue college. (e) Seven cars of the same make, model, and year were sampled for their gas milage. The sample had a mean gas milage of I= 23.21 mpg, with a sample standard deviation of s= 1.66.

Answer 1

Sample size (n) 10. proportion of sample that appeared Mayors action (1) = 7 -0.4 . 99% c.l for the prope of popel - & Zoo, J (1.4) - 0.7 79.546*10-4 (1-08) - 10 - On 7 F 0.37 . : 0.327, 2013) d sample size (n)- 200. prop? of ua that do not plan to continue college ( ) = 450 0.225 99% C'I for prope is- u § 7 Zona -6°01 P(1-A) 2 0 225 2.5.16 0.225 (101225) 900 2 (0.295 I 0.046) = (s. 1499, 0.301)