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.

No, we cannot infer anything about the population as the sample is likely to be unbiased

Yes, we can make inferences about the population as the sample is likely to be unbiased

Yes, we can make inferences about the population as the sample is likely to be biased

No, we cannot infer anything about the population as the sample is likely to be biased

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.

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 $H_0$

Lower levels like $\alpha = 0.00001$ may unnecessarily complicate results by demanding extreme evidence before rejection.

A conservative approach of choosing a moderately low but not excessively stringent value such as $\alpha = 0.02$ provides a balance between detecting effects and avoiding mistakes.

Using a very high alpha level such as $\alpha = 0.25$ can increase the chances of committing a Type II error while decreasing the power (false positive rate) incorrectly reject the true null.

A common choice like $\alpha = 0.01$, $\alpha = 0.05$, or $\alpha = 0.1$ are possible choices depending on the desired strictness against Type I errors.

Handling comparisons separately risks inflating Type I errors due to multiplicity without adjusting significance levels across simultaneous tests.

By conducting separate tests instead, sample sizes effectively decrease leading to potentially inconclusive results.

Separate tests eliminate chances of committing any statistical errors compared to a joint approach provided data randomization is adhered to properly.

One risks encountering confounding variables influencing preferences inadvertently favoring whichever lunch option tested first.

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.