Question

A statistical test is conducted to see if there is evidence that the proportion of US citizens who can name the capital city of Canada is greater than 0.75. Use the following possible sample results Sample A: 38 successes out of 40 Sample B: 31 successes out of 40 Sample C: 34 successes out of 40 Sample D: 27 successes out of 40 (a) State which of the possible sample results provides the most significance evidence for the claim Sample A Sample B Sample C Sample D SHOW HINT LINK TO TEXT (b) State which (if any) of the possible results provide no evidence for the claim Sample A Sample B SempleC Sample D None

Answer 1

Sample A, with 38 successes out of 40, provides the most significant evidence for the claim that the proportion is greater than 0.75, while Sample D, with 27 out of 40 successes, provides no evidence for the claim.

Step-by-step explanation:

A hypothesis test to see if the proportion of US citizens who can name the capital city of Canada is greater than 0.75 is conducted using various sample results. When comparing Sample A (38 successes out of 40) to Samples B (31 out of 40), C (34 out of 40), and D (27 out of 40), Sample A provides the most significant evidence for the claim because it has the highest proportion of successes (38/40 = 0.95), which is substantially greater than 0.75.

On the other hand, Sample D (27 out of 40 = 0.675) provides no evidence for the claim since its success rate is less than 0.75. Therefore, Sample D is actually evidence against the claim that the proportion is greater than 0.75.

A hypothesis test could be a test of means or proportions. Considering we're dealing with success rates, this is a test of proportions. When the data involve categorizing into 'success' or 'failure' and we must infer about a population proportion, a test of proportions is used.

Answer 2

a) Sample A

b) Sample D

Step-by-step explanation:

The sample that will provide the most significance evidence for the claim is the one that has the bigger proportion of US citizens who can name the capital city of Canada.

The sample that has the bigger proportion is Sample A, with p=38/40=0.95.

The samples that have a proportion of 0.75 of less surely will give no evidence for the claim.

The sample D has a proportion of p=27/40=0.675, which is less than 0.75, so it doesn't provide evidence for the claim.

Sample C has a proportion of 0.775. Is very close to 0.75, but its value as evidence depends on the level of significance of the test.