# 5-1 Discussion: Applications of Two-Sample Tests

I’m working on a Mathematics question and need guidance to help me study.

For your initial post, choose one of the following two prompts to respond to. Then in your two follow up posts, respond at least once in each option. Use the discussion topic as a place to ask questions, speculate about answers, and share insights. Be sure to embed and cite your references for any supporting images.

Write a confidence interval or hypothesis test problem using one of the options below. For whichever option you choose, gather appropriate data and post your problem (without a solution) in the discussion topic. You may add another sample to the data that you gathered in your Module Three Discussion Topic post. Allow time for your classmates to post their solutions, and then respond to your own post with a solution for others to check their work.

Option 1:

Think of a problem that you may be interested in that deals with a comparison of two population means. Propose either a confidence interval or a hypothesis test question that compares these two means. Gather appropriate data and post your problem (without a solution) in the discussion topic. Later, respond to your own post with the solution for others to check their work.

For example, you may want to know if the average weight of a rippled potato chip is the same as the average weight of a non-rippled potato chip. You may weigh rippled regular potato chips from a large bag and find weights of 1.7, 1.9, 2.4, 1.3, 1.7, and 2.0 grams. You may weigh non-rippled potato chips from another large bag and find weights of 1.8, 1.6, 1.9, 1.9, and 1.4 grams. Assume a random sample was drawn.

Option 2:

Think of a problem that you may be interested in that deals with a comparison of two population proportions. Propose either a confidence interval or a hypothesis test question that compares these two proportions. Gather appropriate data and post your problem (without a solution) in the discussion topic. Later, respond to your own post with your own solution.

For example, you may believe that the proportion of adults in California who are vegetarians is more than the proportion of adults in New Hampshire who are vegetarians. In two independent polls, you may find that 109 out of 380 California residents are vegetarians and 39 out of 205 New Hampshire residents are vegetarians.

For your response to a classmate (two responses required, one in each option), solve your classmate’s confidence interval or hypothesis test problem, using a significance level not previously used Make sure that you use appropriate terminology and specify whether you are using the classical method or the p-value method.

To complete this assignment, review the Discussion Rubric document.

This is what my professor said to do with this discussion.

WEEK 5 DISCUSSION BOARD PROMPT

For the discussion boards, two options are given for you to choose from for your initial post. In your response posts, you are required to respond at least once to each option.

Like Week 4, this week you should have a minimum of four posts in total:

1. Your initial post to either Option One or Option Two
2. After allowing time for your classmates to post their solutions, respond to your own post with the solution.
3. A response to one of your peers’ responses to Option One
4. A response to one of your peers’ responses to Option Two

In your title for your discussion post, please clearly include which option you are answering by typing “Option One: [your title]” or “Option Two: [your title].”

As a part of your initial post, it is required for you to post your answer to the problem for your peers to check their work against in your responses. The discussion boards response posts will be hidden from your view until you make your own post first.

Please watch the following video for additional help and direction with these posts:

Notes on Discussion Board 5

OPTION ONE NOTES:

• You should use proper statistic language for hypothesis testing OR confidence intervals comparing TWO population means
• You should pick a significance level to use
• Your two different samples should be clearly identified

OPTION TWO NOTES:

• You should use proper statistic language for hypothesis testing OR confidence intervals comparing TWO population proportions
• You should pick a significance level to use
• Your two different samples should be clearly identified

FOLLOW-UP RESPONSE NOTES:

• Confidence Intervals: You should clearly define your solution in terms of your confidence % with your upper and lower bound defined with your units, similar to the one found in Week 3:
We are [X]% confident that the true population mean [for whatever your problem defines] is between [lower bound] and [upper bound] [units].
• Hypothesis testing: Be sure to include all parts of hypothesis in your response to your peers and to your original problem:
• Null and alternative hypothesis
• Alpha significance Level
• Classical Method: Test-statistic and Critical Value
• P-value Method: P-value and comparison to your Critical Value at your Alpha significance level
• Conclusion (i.e. whether you reject or not reject the null hypothesis)

EXAMPLE OF DISCUSSION BOARD POST:

Question (Initial Discussion Board post, using the example for proportion provided): You believe that the proportion of adults in California who are vegetarians is more than the proportion of adults in New Hampshire who are vegetarians. In two independent polls, you may find that 109 out of 380 California residents are vegetarians and 39 out of 205 New Hampshire residents are vegetarians.

Follow-up (To your Initial post and to your Classmates’ posts):

Your response should contain all parts shown:

P1 = 109/380 = 0.2868

P2 = 39/205 = 0.1902

P = (109+39)/(380+205) = 0.2530

1. H0: P1 = P2
H1: P1 > P2
2. This is a right tailed-test as the alternative hypothesis is less. The critical value associated with alpha = 0.05 is 1.645.
3. Classical Method:
Z-Test Statistic = [(0.2868 – 0.1902) –0] / [sqrt{[0.2530]*[1 – 0.2530]*[(1/380)+(1/205)]}]

= [0.0966] / [sqrt{[0.2530]*[0.7470]*[0.0075096]}]
= [0.0966] / [sqrt{0.00141492}]

= [0.0966] / [0.0376723]
= 2.5642
Since 2.56 > 1.645 IS a true statement, we do REJECT the null hypothesis.

1. P-Value Method:
P-value = 0.0052
If our p-value is less than or equal to our alpha significance level, we will be able to reject the null hypothesis. However, since 0.0052 < 0.05 IS true, we do REJECT the null hypothesis.
2. Conclusion:
There is enough evidence to reject the null hypothesis.
Therefore, there is enough evidence to claim that the proportion of adults who are vegetarians in California is greater than the proportion of adults who are vegetarians in New Hampshire at the significance level of alpha = 0.05.

I also was told not to post the answer to the problem, but I will still need the answer with the post.

I will need two responses done on 2 different classmates posts but I will post them after I get my initial post.