Quiz 7

Explain what the phrase 95% confident means when we interpret a 95% confidence interval for population mean. A. In repeated sampling, 95% of similarly constructed confidence intervals contain the value of the population mean. B. 95% of the observations in the population fall within the bounds of the calculated interval. C. 95% of similarly constructed confidence intervals would contain the value of the sampled mean. D. The probability that the sample mean falls in the calculated interval is 0.95.

A. In repeated sampling, 95% of similarly constructed confidence intervals contain the value of the population mean.

A statistic is biased if the mean of the sampling distribution is equal to the parameter it is intended to estimate. True False

False

Of all possible unbiased estimators for a population parameter, the estimator that is the minimum variance unbiased estimator (MVUE) has the largest variance. True False

False

What does it mean for an estimator to be consistent? A. As the sample size gets larger and larger the estimates ultimately get closer and closer (i.e. converge) to the true value of the parameter. B. As the sample size gets smaller and smaller the estimates ultimately get closer and closer (i.e. converge) to the true value of the parameter. C. Of all possible unbiased estimators for a population parameter, the estimator that is the minimum variance unbiased estimator (MVUE) has the largest variance. D. The expected value (theoretical mean) of the estimator equals the parameter we are estimating.

A. As the sample size gets larger and larger the estimates ultimately get closer and closer (i.e. converge) to the true value of the parameter

A random sample of 16 measurements was selected from a population that is approximately normally distributed produced sample mean = 97.94 and sample standard deviation = 12.64. If we construct 80% and 95% confidence intervals (CI) for population mean form the data, which statement is true? A. The width of both of these CIs for population mean will be exactly the same. B. 80% CI will be wider than the 95% CI for population mean. C. 80% CI will be narrower than the 95% CI for population mean.

C. 80% CI will be narrower than the 95% CI for population mean

A sample of 36 commuters in Chicago showed the sample average of the commuting times was 33.2 minutes and the sample standard deviation was 8.3 minutes. A researcher is interested in finding a 99% confidence interval of true average commuting times in Chicago. What is an appropriate population parameter in this setting? A. Sample mean B. Population proportion C. Population mean D. Sample proportion

C. Population Mean

A random sample of 250 students at Indiana University finds that these students take an average of 15.6 credit hours per semester with a standard deviation of 2.1 credit hours. The 98% confidence interval for the true mean is 15.6 ± 0.309 (i.e. sample mean ± margin of error). Interpret the confidence interval. A. The probability that a student takes 15.291 to 15.909 credit hours in a semester is 0.98. B. We are 98% confident that the average number of credit hours per semester of the sampled students falls in the interval 15.291 to 15.909 hours. C. We are 98% confident that the true average number of credit hours per semester taken by Indiana University students falls in the interval 15.291 to 15.909 hours. D. 98% of the students take between 15.291 to 15.909 credit hours per semester.

C. We are 98% confident that the true average number of credit hours per semester taken by Indiana University students falls in the interval 15.291 to 15.909 hours.

If all else remain the same, which of the following will make a confidence interval for the population mean narrower? I. Decrease the confidence level II. Decrease the sample size III. Decrease the margin of error A. I only B. II only C. II and III D. I and III

D. I and III

if all else remains the same, which of the following will make a confidence interval for the population mean wider? I. Increase the confidence level II. Increase the sample size III. Decrease the margin of error A. I and III B. I and II C. II only D. I only

D. I only

A point estimator of a population parameter is a rule or formula which tells us how to use sample data to calculate a single number that can be used as an estimate of the population parameter True False

True