Question

1.) A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Which of the following interpretations is correct?

Select one:

A. 90% of the sampled students are female.

B. We are 90% confidence that proportion of all statistics female students falls in the interval 0.438 to 0.642

C. 90% of all statistic students are female.

D. We are 90% confident that the sample proportion of statistics female students falls in interval 0.438 to 0.642.

2.)The Friday after Thanksgiving is the biggest shopping day of the year. You are interested in the number of people who claim to have finished their Christmas shopping at the end of this weekend. On Monday, you take a random sample of people by standing at a toll booth at 7:00 a.m. and asking every third commuter if he or she has finished Christmas shopping. Based on the last year's data, you expect approximately 10% to claim completion of Christmas shopping. How many commuters must you sample of a 95% interval estimate to have a margin of error of +3%?

Select one:

A. 269

B. 384

C. 385

D. 268

Answer 1

Solution,

1) The 90% confidence interval: (0.438, 0.642)

correct option is = B

B. We are 90% confidence that proportion of all statistics female students falls in the interval 0.438 to 0.642

2) = 0.10

1 - = 1 - 0.10 = 0.90

margin of error = E = 0.03

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.96 / 0.03)2 * 0.10 * 0.90

= 384.16

sample size = n = 385

correct option is = C