Proportions
In order to carry out a test for the difference in population proportions based on independent random samples without bias, what condition relating to sampling methods should have been followed?
Samples should consist only of volunteers who are available at convenient times.
Samples should come from pre-determined quotas representing specific segments within each population.
Samples must have been selected independently from each other using random sampling methods.
Samples should include every fifth individual from an ordered list until sample size requirements are met.
To determine if there is a significant difference between the proportions of males and females who prefer online shopping, which of the following sample sizes would most likely produce a more reliable test result?
100 males and 100 females
10 males and 10 females
1000 males and 1000 females
50 males and 200 females
Which outcome would suggest greater variability than expected when performing a test for difference between two population proportions?
A smaller p-value leading to rejection of the null hypothesis at common alpha levels.
Observed proportion differences aligning closely with those presupposed by a null hypothesis.
A larger-than-expected standard error relative to estimated proportion differences.
Sample sizes that are exactly equal across groups being compared in a study design.
When comparing two sample proportions to determine if there's a significant difference, what statistic do we use?
Z-score
Chi-square statistic
T-score
F-statistic
If you flip a fair coin once, what is the probability of getting heads?
0.5
0
1
Cannot be determined from the given information
A statistics student is conducting a hypothesis test for the difference in two population proportions. They calculate a p-value of 0.02. What can they conclude?
Reject the null hypothesis and conclude that there is no statistically significant difference between the two population proportions
Reject the null hypothesis and conclude that there is a statistically significant difference between the two population proportions.
Fail to reject the null hypothesis and conclude that there is a statistically significant difference between the two population proportions
Fail to reject the null hypothesis and conclude that there is no statistically significant difference between the two population proportions
What requirement must both samples meet to perform an appropriate test comparing their proportions?
Each sample must contain exactly half males and half females.
Both samples must be independent.
Samples need to have been taken at exactly the same time period.
They must come from populations with identical variances.

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If the conditions for inference about the difference between two population proportions are not met due to a small sample size, which of the following is an appropriate next step?
Increase the confidence level to compensate for small sample size.
Apply a one-sample t-test instead of a two-proportion z-test.
Use a simulation-based approach to estimate the sampling distribution and p-value.
Use the Central Limit Theorem to assume that the sampling distribution is approximately normal.
What statistical test do we use to compare two population proportions to determine if they are significantly different from each other?
Two-proportions z-test
Paired samples t-test
One-sample t-test
Anova f-test
Which one of these would not affect the probability when performing hypothesis tests about differences between two population proportions?
None - all factors affect the probability
The number of observations
The standard deviation
The significance level