Estimates and Sample Sizes Statistics

A confidence interval estimate is determined from the summer earnings of a SRS of n students. All other things being equal, which of the following will result in a smaller margin of error?

• greater confidence level

• larger sample standard deviation

• larger sample size

• Introducing bias into sampling

Two confidence interval estimates from the same sample are (0.72, 0.83) and (0.75, 0.81). One is at 95%, the other is at 99%. Which is which?

• (0.72, 0.83) is at 99%

• (0.72, 0.83) is at 95% 

• Need to know sample size to determine this

• Need to know standard error to determine this

Which of the following is true pertaining to a 2-proportion z-interval?

• There are no restrictions on sample size 

• This interval can be found even if the samples are not random

• The population should be large, relative to each of the sample sizes

• So long as all conditions are met for one sample, you do not need to check conditions for the other sample

Conduct a test to determine whether or not the population proportion of voters in favor of proposal A is greater than 50%. In a random sample of 200 voters, 140 said that they were in favor of this proposal. Compute the test statistic.

• z = 6.17

• z = 5.66

• z = 19.80

• None of the above

A sample of 600 ninth graders was selected at random and asked how much time they spend on homework each day. Of the ninth graders selected, 220 spend less than 2 hours on homework each day. If the conclusion was drawn that “approximately 1.35 million ninth graders spend less than 2 hours on homework each day,” which of the following is closest to the population, in millions, of ninth graders?

• 0.368

• 0.495

• 3.68

• 5.84

Why is a sample of 1000 people better than a sample of 100 people?

• It reduces the margin of error.

• It decreases bias.

• Having more people is always better.

• More people means that our results are more accurate.

If no p-hat value is given, what should you assume p-hat equals?

• 0.01

• 0.05

• 0.10

• 0.5

A 99% confidence interval found that the true proportion of teens who drink coffee every day is in the interval (0.785, 0.831). What was the p^ value used to determine this interval? 

• 0.8

• 0.808

• 0.825

• 0.831

In a past General Social Survey, a random sample of men and women answered the question “Are you a member of any sports clubs?” Based on the sample data, 95% confidence intervals for the population proportion who would answer “yes” are .13 to .19 for women and .247 to .33 for men. Based on these results, you can reasonably conclude that 

• At least 25% of American men and American women belong to sports clubs.

• At least 16% of American women belong to sports clubs. 

• There is a difference between the proportions of American men and American women who belong to sports clubs.

• There is no conclusive evidence of a gender difference in the proportion belonging to sports clubs

Which statement is true?

• Statement A only

• Statement B only

• Statements A and B

• Neither A nor B