stats exam 2

Why is it not possible to have 100% confidence? Explain.

A. A 100% confidence interval is not possible unless either the entire population is sampled or an absurdly wide interval of estimates is provided.

A market researcher collects a simple random sample of customers from a population of over a million customers that use a home improvement website. After analyzing the sample, she states that she has 95% confidence that the mean time customers spent on that website per day is between 15 and 56 minutes. Suppose that the population mean time customers spent on that website is 59 minutes a day. Does this value of the population mean help to show that the confidence interval estimate is correct? Explain.

A. No, because the population mean, μ, is not included within the confidence interval estimate.

If you use a 0.05 level of significance in a (two-tail) hypothesis test, the decision rule for rejecting H0: μ=11.2, if you use the Z test, is shown below. Reject H0 if ZSTAT<−1.96 or ZSTAT>+1.96. What is your decision if ZSTAT=+2.09?

A. Since ZSTAT falls into the rejection region, reject H0.

If, in a (two-tail) hypothesis test, the p-value is 0.1351, what is your statistical decision if you test the null hypothesis at the 0.07 level of significance?

A. Since the p-value is greater than α, do not reject H0.

If, in a sample of n=47 selected from a right-skewed population, X =67 and S=24, would you use the t test to test the null hypothesis H0: μ=60?

A. Yes, you would use the t test because the sample size is at least 30 and this population size allows for the Central Limit Theorem to take effect.

How do you interpret a coefficient of determination, r2, equal to 0.05?

B. The interpretation is that 5% of the variation in the dependent variable can be explained by the variation in the independent variable.

In the Country A legal system, a defendant is presumed innocent until proven guilty. Consider a null hypothesis, H0, that the defendant is innocent, and an alternative hypothesis, H1, that the defendant is guilty. A jury has two possible decisions: Convict the defendant (i.e., reject the null hypothesis) or do not convict the defendant (i.e., do not reject the null hypothesis). Explain the meaning of the risks of committing either a Type I or Type II error in this example.

C. A Type I error would be incorrectly convicting the defendant when he is innocent. A Type II error would be incorrectly failing to convict the defendant when he is guilty.

If you use a 0.06 level of significance in a (two-tail) hypothesis test, what is your decision rule for rejecting a null hypothesis that the population mean is 450 if you use the Z test?

D. Reject H0 if ZSTAT<−1.88 or ZSTAT>+1.88.

ssuming that the population is normally distributed, construct a 99% confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range. Sample A: 1 1 2 4 5 7 8 8 Sample B: 1 2 3 4 5 6 7 8 Explain why these two samples produce different confidence intervals even though they have the same mean and range.

D. The samples produce different confidence intervals because their standard deviations are different.

what is the meaning of r2?

D. r2 •100% of the variation in the dependent variable can be explained by the variation in the independent variable.