Stat Lab 6.1 and 6.3 PDF

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Stat lab 6.1 and 6.3 - use for reference...

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LAB 6.1 &63 Statistics 200: Lab Activity for Sections 6.1 and 6.3 Inference for proportion(s) using a normal distribution – Learning objectives:  

Recognize when a question calls for inference for a single proportion or a difference in proportions Recognize when a normal distribution is an appropriate model to use

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Use statistical software such as Minitab to perform a hypothesis test and construct a confidence interval for a proportion or a difference in proportions

Note: We’ll be using Minitab quite heavily throughout Chapter 6. Don’t forget to Remember to refer to our Minitab Users Guide to see how to conduct an analysis for a given situation.

Metal tag on a penguin

One penguin tagging another

Does tagging penguins with metal tags, as opposed to electronic tags, harm them? Scientists took 100 penguins and randomly chose half of them to be tagged with metal tags and half to be tagged with electronic tags. They followed the penguins for 10 years, and found that 10 of the metal-tagged penguins survived, as opposed to 18 of the electronic tagged penguins. They also collected data on whether the penguins successfully produced offspring in each of the possible breeding seasons. Activity 1: For each situation, decide if it warrants (a) inference for a single proportion (one categorical variable), or (b) inference for a difference in proportions (two categorical variables). 1. Of all the penguins, compare the proportion who survived to the proportion who did not survive. single 2. Compare the proportion of metal-tagged penguins who survived to the proportion of electronictagged penguins who survived. two 3. Did a greater proportion of breeding seasons result in offspring or no offspring? single 4. Did metal or electronic tagged penguins have a greater proportion of successful offspring? single

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LAB 6.1 &63 (Hint: When thinking through each of these, remember to focus on the variables. Does the question involve one or two categorical variables?)

Activity 2: Normal-Based Inference from Summarized Data: Tag Type and Survival Compare the proportion of metal-tagged penguins that survived to the proportion of electronic-tagged penguins that survived. 1. Is the use of the normal distribution for inference appropriate here? Why or why not? a. yes 2. Use Minitab to conduct inference for 2 proportions based on these summarized data, and answer the following questions using the resulting output. Copy and paste the resulting output here. 3. What is the sample difference in proportions, proportion of metal-tagged penguins who survive – proportion of electronic-tagged penguins who survive? .2 - .36 = -.16 4. What is the 95% confidence interval for this difference? -.333188 - .013188 5. In Minitab the default confidence level is 95%. To change this, rerun the inference again, but before clicking “OK” click on “Options” and change the confidence level to 90%. What is the 90% confidence interval for the difference in proportions? -.305344 - -.014656 6. What is the default p-value for the two-sided hypothesis test for a difference using the normal distribution, if you didn’t change any of the options? .07 (fishers: .118) 7. When you conduct a hypothesis test, you want to see how extreme the results are if the null hypothesis is true. This means assuming the two proportions are the same. In order to properly reflect this when calculating the p-value, conduct the test in Minitab again, but before clicking “OK”, click Options, and change the test method to “Use the pooled estimate of the proportion.” Now what is the Normal-based p-value for the test? .075 (fishers: .118) NOTE: When testing for a difference in proportions using Minitab, you should always change this option to Test Method: Use the pooled estimate of the proportion. 8. The default in Minitab is to do a two-sided hypothesis test, but in this case, the researchers were really interested in answering the question: “Does tagging penguins with metal tags, as opposed to electronic tags, harm them?”. What is the appropriate alternative hypothesis? Ha: p1 < p2 9. Conduct the test again, but before clicking “OK”, click Options and choose the appropriate alternative hypothesis. Now what is the Normal-based p-value for the test? .037

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LAB 6.1 &63 10. Based on your answer to #9, make a generic conclusion about the null hypothesis and a conclusion in context about the alternative hypothesis. Reject null 11. Based on your conclusion and the data collection, can we conclude that metal tags, as opposed to electronic, cause fewer penguins to survive? yes

Activity 3: Normal-Based Inference from Raw Data: Tag Type and Breeding Success The data relevant to breeding success are available in Penguins.mwx. Each row corresponds to a possible breeding season for a particular penguin. 1. Is the normal distribution appropriate to use here? Why or why not? yes, n times p hat > 10 2. Use Minitab to conduct inference for two proportions based on the two categorical variables: whether the breeding season resulted in successful offspring (Offspring) broken down by tag type (Tag). Copy and paste the resulting output here. 3. How many possible breeding seasons did the metal tagged penguins have? How many of these resulted in successful offspring? For metal tagged penguins, what is the sample proportion of breeding seasons resulting in successful offspring? Possible metal: 122, successful metal: 39, p hat: .319672 4. Which group had a higher proportion of successfully having offspring – those with metal or electronic tags? electronic 5. What is the difference in proportions? Based on your answer to #4, which way is Minitab calculating the difference in proportions? (electronic – metal, or metal – electronic)? .124078, electronic - metal (Note: If Minitab calculates the difference in proportions from a spreadsheet, make sure you pay attention to which order the subtraction is done, as this is crucial for understanding results! If you aren’t sure, look at the individual group sample proportions to understand the difference. It’s also important to use this same ordering for determining the correct inequality in the alternative hypothesis.) 6. Scientists hypothesized that the metal tags may harm breeding chances. State the relevant hypotheses, using the same ordering that Minitab used to calculate the difference in proportions. Ho: p1 = p2, Ha: p1 > p2 7. Conduct the hypothesis test with the appropriate alternative hypothesis. What is the normal-based p-value? .017

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LAB 6.1 &63 8. Based on this p-value, make a generic conclusion about the null hypothesis and a conclusion in context about the alternative hypothesis. Reject the null 9. How large is the difference? Give a 99% confidence interval. Diff: .124078, -.024460 - .2726216 (Hint: If you’ve changed the alternative hypothesis in Options, make sure you always change the options back to the two-sided alternative hypothesis before running a confidence interval, otherwise you will get a one-sided confidence interval, which is rarely what you want. Confidence intervals should always include both a lower and an upper bound.)

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