Confidence Intervals (all single samples + finding n)

You have sampled 25 students to find the mean SAT scores at Morris Knolls High School. A 95% confidence interval for the mean SAT score is 900 to 1100. Which of the following statement gives a valid interpretation of this interval?

• 95% of the 25 students have a mean score between 900 and 1100.

• 95% of the population of all students at Morris Knolls have a score between 900 and 1,100.
• If this procedure were repeated many times, 95% of the resulting confidence intervals would contain the true mean SAT score at Morris Knolls.
• There's a 95% chance that the true mean is between 900 and 1100

A research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend exercising each week. They want to estimate the mean within a margin of error of 0.5 hours with a 95% level of confidence. Previous data suggests that the standard deviation of the population is 2.2. Which of the following is the smallest sample size they could use?

• 60
• 75
• 90
• 180

A 90% confidence interval for a population mean is determined to be 800 to 900. If the confidence is increased to 95% confidence while the sample statistics and sample size remain the same, the confidence interval

• becomes wider
• becomes narrower
• does not change

Ms. Peterson takes a simple random sample of students at Mayo High School and finds that 71% of her sample went to the basketball game on Tuesday.  She wants to estimate the true proportion of students who went.  Which distribution should she use?

• z distribution for means
• t distribution for means
• z distribution for proportions
• none of these

Researchers are trying to estimate the mean weight (in pounds) of professional athletes in the US.  They take a sample of athletes and find the mean and standard deviation of the sample.  Which distribution should they use to construct the confidence interval?

• z distribution for means
• t distribution for means
• z distributions for proportions
• none of these

A researcher wishes to estimate the proportion of Americans who have visited an entertainment theme park near Orlando within the last five years.  He wishes to do this with 95% confidence with a margin of error of 0.05 or less.  Which of the following is the smallest size that he could use?

• 40
• 212
• 324
• 385

You plan to construct a 92% confidence interval.  What critical value should you use?

• .08
• 1.96
• .04
• 1.75

You take a poll and find that 34% of the 100 people you asked dislike school lunches. What is the standard error?

• 0.093
• 0.047
• .034
• .34

You make a histogram of some data and find that it is not normally distributed indicating that the population is likely not normal.  Your sample size is 50, and the mean of your data is 76.  What should you use for a confidence interval?

• z distribution
• t distribution
• neither