Proportions

Population data

Sample data

A known population proportion

A random sample

Larger sample sizes have no effect on the width of confidence intervals for proportions.

It variably affects width depending on whether or not outliers are present in larger samples.

It increases width due to greater variability introduced by more data points.

It reduces the width making it more precise because standard error decreases with larger sample sizes.

The width remains the same

The width depends on the confidence level

The width tends to increase

The width tends to decrease

Wider confidence intervals always lead to more accurate conclusions about population characteristics than narrower ones even if overlap occurs.

Narrower intervals have no effect on claims because they simply reflect less variability within sample data points around an estimate.

Narrower intervals increase precision but reduce certainty in claiming differences or similarities between populations due to smaller margins of error.

Such result conclusively supports hypothesis because several outcomes actually encapsulate expected number.

This implies there’s definite proof against hypothesis since at least one sampled interval doesn't contain proposed figure.

The inconsistency invalidates entire experiment necessitating redesign before drawing any conclusions whatsoever.

It suggests uncertainty around whether or any true difference exists from hypothesized value as some samples seem consistent while others don't.

To guarantee that all subgroups are equally represented in the sample size.

To minimize bias in estimating the population parameter.

To justify using different types of statistical tests on collected data sets.

To ensure that there are no outliers in the collected data set.

The sample proportion is an accurate estimate of the population proportion

The sample is representative of the population

The confidence level is high

The true population proportion is within the estimated range

There is strong evidence to claim that more high school students prefer physical textbooks than online ones.

The data suggests that no high school student prefers physical textbooks over online ones.

There is convincing evidence that exactly half of the high school students prefer online textbooks.

There is insufficient evidence to claim that a majority of high school students prefer online textbooks.

The calculation method used by researchers to construct these intervals must be flawed since they exclude $p=0.50$.

All individuals within each sampled population have identical views on recycling since none include $p=0.50$.

Recycling preference varies widely across populations because there's inconsistency in including $p=0.50$.

It suggests that most likely, more or fewer than half of the population sampled are willing to recycle rather than exactly half.

The confidence level

The sample proportion

100%

The margin of error