C955 Applied Probability and Statistics - Set 2 - Part 2

Correct Answer: The interval becomes wider

Greater confidence requires capturing more possibilities, so raising the confidence level from 95 to 99 percent widens the interval.

Correct Answer: It becomes narrower

Larger samples reduce the standard error, producing narrower intervals and therefore more precise estimates at the same confidence level.

Correct Answer: The amount added and subtracted from the point estimate to form the interval

The margin of error is the half-width of a confidence interval, reflecting the precision of the estimate at the chosen confidence level.

Correct Answer: 49% to 55%

The interval extends the margin of error in both directions: 52 minus 3 gives 49, and 52 plus 3 gives 55.

Correct Answer: The interval includes values where the apparent lead would reverse

If the plausible range spans values below 50 percent, the data cannot establish a genuine majority, so the apparent lead is not statistically meaningful.

Correct Answer: A statement of no effect or no difference that is tested

The null hypothesis states there is no effect or difference. Statistical testing evaluates whether the data provide sufficient evidence against it.

Correct Answer: The claim that there is an effect or difference

The alternative hypothesis expresses the effect the researcher is investigating and is accepted as supported only if the null hypothesis is rejected.

Correct Answer: The probability of results at least as extreme as observed, assuming the null is true

A p-value quantifies how surprising the data would be if the null hypothesis were true. It is not the probability that the null hypothesis is correct.

Correct Answer: Reject the null hypothesis

A p-value below the chosen significance level indicates the data are unlikely under the null hypothesis, providing grounds to reject it.

Correct Answer: A 5% risk of rejecting a true null hypothesis

The significance level is the probability of a Type I error, meaning rejecting the null hypothesis when it is actually true.

Correct Answer: Rejecting a null hypothesis that is actually true

A Type I error is a false positive: concluding an effect exists when in reality it does not. Its probability equals the significance level.

Correct Answer: Failing to reject a null hypothesis that is actually false

A Type II error is a false negative: failing to detect a real effect. Its probability decreases as sample size and effect size increase.

Correct Answer: The probability of correctly rejecting a false null hypothesis

Power is the probability of detecting an effect that genuinely exists, equal to 1 minus the probability of a Type II error.

Correct Answer: Increasing the sample size

Larger samples reduce sampling variability, making genuine effects easier to detect and thereby increasing power.

Correct Answer: Absence of evidence may reflect insufficient power rather than absence of effect

A non-significant result may mean no effect exists or that the study lacked power to detect a real one, so it does not establish the null as true.

Correct Answer: A result can be statistically significant yet too small to matter practically

With large samples, trivially small effects can achieve statistical significance, so the magnitude of the effect must be judged separately for practical relevance.

Correct Answer: A measure of the magnitude of a difference or relationship

Effect size quantifies how large an observed difference or association is, complementing the p-value which addresses only whether an effect is detectable.

Correct Answer: Testing for a difference in one specified direction only

A one-tailed test examines whether a parameter is specifically greater or specifically less than a value, concentrating the rejection region in one tail.

Correct Answer: When a difference in either direction is of interest

A two-tailed test detects departures in either direction and is the appropriate default unless there is strong prior justification for a directional hypothesis.

Correct Answer: Means, typically when the population standard deviation is unknown

A t-test compares means using the sample standard deviation, employing the t-distribution which accounts for the added uncertainty of estimating variability.