Which of the following is NOT a prerequisite condition for conducting a two-proportion hypothesis test?

Using a TI-84, which function should you select to perform a hypothesis test for two proportions?

A 90% confidence interval for p1 - p2 is (0.03, 0.14). What conclusion can be drawn about the claim that p1 = p2?

What is the least number of data points $\left(n\right)$ required in each sample when conducting a Wilcoxon rank sum test to ensure appropriate statistical inference?

Which of the following is NOT an assumption required for a valid two-sample t-test with unknown and unequal variances?

To evaluate battery life between two types of wireless headphones, a technician tests $20$ units of Brand A and $25$ units of Brand B.

Brand A has a mean battery life of $18.2$ $\text{hours}$ with a known population standard deviation of $1.5$ $\text{hours}$.

Brand B has a mean battery life of $17.5$ $\text{hours}$ with a known population standard deviation of $1.8$ $\text{hours}$.

At the $\alpha =0.05$ level of significance, can the technician conclude that there is a significant difference in the average battery life between the two brands?

An analyst is comparing the consistency of customer satisfaction scores between two branches of a retail store. A sample of $14$ scores from Branch X has a standard deviation of $18.7$, and a sample of $11$ scores from Branch Y has a standard deviation of $22.3$. At $\alpha =0.05$, is there evidence to suggest the standard deviations are not equal?

A nutritionist claims that the average sugar content in Brand A cereal is greater than the average in Brand B cereal. To test this claim at the $\alpha =0.01$ level of significance, the following data is collected from independent random samples of each brand:

Population standard deviations:

${\sigma }_1=1.5$ grams (Brand A), ${\sigma }_2=1.2$ grams (Brand B)

Sample statistics:

${\bar{x}}_1=10.2$ grams, $n_1=64$ (Brand A)

${\bar{x}}_2=9.6$ grams, $n_2=49$ (Brand B)

A 95% confidence interval for μ1 - μ2 is (1.2, 5.8). What does this interval indicate about the claim that μ1 = μ2?

A matched pairs study has n = 25 pairs. What are the degrees of freedom for the t-distribution?

Given the differences from a matched pairs study: [3, 5, 2, 4, 6], calculate the sample standard deviation of the differences.

A matched-pairs study evaluated a typing tutor's effect on speed. For $6$ participants, the differences (post-tutor minus pre-tutor) in typing speeds are:

Mean difference: $(\bar{d}=1.8)$ words per minute

Standard deviation of differences: $(s_d=1.5)$ words per minute

Sample size: $(n=6)$

Calculate the test statistic for a right-tailed hypothesis test of the claim that the typing tutor increases typing speed.

A company wants to know if a new training program increases employee productivity. $10$ employees' productivity scores before and after the program are recorded. At $\alpha =0.01$, is there sufficient evidence to conclude that the program increases productivity? Assume normality.

A researcher wants to test if a diet leads to weight loss. The differences are calculated as (before - after). Which set of hypotheses is appropriate?

In a study measuring stress levels before and after yoga sessions, researchers plan a left-tailed test using a dependent sample of $12$ participants. What is the critical $t$-value at the $0.05$ significance level, and what is the rejection region?