Proportions

It determines whether a confidence interval can be constructed.

It decreases the width of the confidence interval.

It increases the width of the confidence interval.

It has no effect on the width of the confidence interval.

The proportion of customers who preferred the old product is significantly higher than the proportion who preferred the new product.

There is no evidence to support a difference in the proportions of customers who preferred the old and new products.

The study is inconclusive and needs to be repeated with a larger sample size.

The proportion of customers who preferred the new product is significantly higher than the proportion who preferred the old product.

Exactly 95% of the sample data falls within this interval.

There is a 95% probability that the observed sample difference is accurate.

We can be 95% confident that the true difference in population proportions falls within this interval.

The two populations' proportions are equal.

If zero falls outside of the range, this means our sample was too small to detect any meaningful differences.

If zero is outside this range, it implies that there is a statistically significant difference between the population proportions of the two groups.

Zero outside the range signifies that effect sizes are large enough to make practical significance irrelevant.

It suggests that we have a large enough sample size such that a significant difference will be present regardless of actual data results.

Median

Standard deviation

Range

Variance

CORRECT. The sample sizes used to calculate both $\hat{p}_1$ and $\hat{p}_2$.

INCORRECT 3. The alpha level used when estimating their initial hypotheses tests.

INCORRECT 1. The calculated values of both sample proportions themselves.

INCORRECT 2. The width of their desired confidence intervals for each proportion.

They must ensure that both samples are independent and randomly selected from their respective populations.

Both samples need not only be large but also exactly equal in size for comparison purposes.

They should check if all individuals in both samples strongly support their candidate without any bias.

It is essential that both samples come from populations with the same standard deviation in opinions.

The proportion of students who prefer literature is higher than the proportion who prefer math.

There is not enough information to draw any conclusions.

There is no evidence to support a difference in the proportions of students who prefer math and literature.

The proportion of students who prefer math is higher than the proportion who prefer literature.

Mode

Mean

Variability

Median

INCORRECT 3. Yes, purely based on the presence of other negative outcome indicators observed during previous analyses purported to predict similar results across study types.

INCORRECT 2. No, because with only a positive point estimate regarded as an indicator for success, no other inferential judgment may be rendered accurate or detailed enough.

INCORRECT 1. Yes, since a negative value always denotes poorer outcomes for target variables being compared in studies usually designed likewise.

CORRECT. No, because a point estimate alone cannot provide enough information without assessing the strength and significance of the statistical analysis.