7. Sampling Distributions & Confidence Intervals: Mean

Estimating the Median Use the sample data listed in Exercise 1 “Bootstrap Requirements” to generate 1000 bootstrap samples, and find the median in each of those samples. After obtaining the 1000 sample medians, find the 95% confidence interval estimate of the population median by evaluating p2.5 and p97.5 from the sorted 1000 medians. Given that the sample times in Exercise 1 are from the 50 times in Data Set 20 “Alcohol and Tobacco in Movies” and those 50 times have a median of 5.5, how well did the bootstrap method work to create a “good” confidence interval?

If we wish to obtain a 95% confidence interval of a parameter using the bootstrap percentile method, we determine the_______percentile and the_______ percentile of the resampled distribution.

Which of the following is not a conclusion of the Central Limit Theorem?

"Simulation IQ scores are known to be approximately normally distributed with mean 100 and standard deviation 15.

a. Simulate obtaining a random sample of 12 IQ scores from this population.

b. Use the data from part (a) to construct a 95% confidence interval for the mean IQ using Student's t-distribution.

c. Use the data from part (a) to obtain at least 2000 bootstrap samples. For each sample, find the mean.

d. Determine an estimate of the standard error of the mean from the bootstrap means found in part (c). Compare this result to the theoretical standard error of the mean, sigma divided by square root of n. Compare this result to the estimate of the standard error of the mean based on the sample data, s divided by square root of n.

e. Construct a 95% confidence interval for the mean IQ using the bootstrap sample from part (c)."

If the confidence level is increased from $90\%$ to $99\%$, what happens to the width of the confidence interval for a population mean, assuming all other factors remain constant?

Suppose you have a data table showing the relationship between hours studied and exam scores. After calculating the regression line, how would you use a regression calculator to make a reasonable prediction for a student who studied $5$ hours?

In the context of probability and statistics, the cumulative distribution function is denoted and defined as which of the following?

Which of the following statements is the best definition of a point estimate?

Normal Quantile Plot The accompanying normal quantile plot was obtained from the longevity times of presidents. What does this graph tell us?

Which distribution should be used to construct a confidence interval for the mean when the sample size is small and the degrees of freedom are $df=5$?

Which of the following accurately describes the critical region in hypothesis testing?

Which of the following is true of the Central Limit Theorem?

Which of the following is a primary benefit of having a large sample size when constructing confidence intervals?

Atkins Weight Loss Program In a test of weight loss programs, 40 adults used the Atkins weight loss program. After 12 months, their mean weight loss was found to be 2.1 lb, with a standard deviation of 4.8 lb. Construct a 90% confidence interval estimate of the standard deviation of the weight loss for all such subjects. Does the confidence interval give us information about the effectiveness of the diet?

In the context of hypothesis testing, what does the $\mathrm{level of significance}$ represent?