Proportions

It improves reliability only if sample mean approaches the sample median.

It has no effect on reliability as standard error is not influential in hypothesis testing.

It may decrease reliability by making it difficult to detect true differences.

It increases reliability by ensuring larger variation in captured sample data.

Population mean (μ)

Sample proportion (p-hat)

Population standard deviation (σ)

Sample mean (x-bar)

The alternative hypothesis claims that the population proportion is greater than 0.5.

The null hypothesis states there's no significant difference between sample and population proportions.

The alternative hypothesis posits the true proportion differs from any value except for 0.5.

The null hypothesis assumes that the population proportion is equal to 0.5.

Inherent variability within student performance masked by averaging scores.

Miscalculation involving critical values stemming from utilizing unconventional significance levels.

Sample selection biases affecting representativeness across various educational contexts.

Failure in addressing potential ethical concerns related directly back towards data collection methodologies.

$\mu$ (mu)

$Ha$ or $H_1$

$\sigma^2$ (sigma squared)

$H_0$ or $H_0$

A two-tailed test should be used

Because we are expecting improvement

We expect a decrease

We expect no change (unchanged performance)

INCORRECT. The mean of scores for all left-handed students

INCORRECT. The percentile rank of the student sample mean

CORRECT. The z-score where both tails of the distribution each contain half of the significance level

INCORRECT. The distance between the mean and the standard deviation times a hundred

Poisson distribution given discrete event occurrences over an interval are being counted.

T-distribution since we're estimating an unknown parameter based on sample data.

Normal distribution due to large enough sample size satisfying conditions for approximation.

Binomial distribution because it describes the number of successes in n independent Bernoulli trials.

One because difference between proportions yields minimal variance.

Zero because observed proportion does not equal hypothesized value.

Negative one indicating strong opposition to public park funding.

Zero because observed proportion equals hypothesized value.

There's conclusive evidence that supports the alternate hypothesis over the null hypothesis.

The null hypothesis is definitely true without doubt.

The alternate hypothesis has been proven incorrect beyond any doubt.

There isn't enough evidence to conclude that the population proportion differs from the specified value.