Section #04.3.1 shared lab

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Pennsylvania State University *

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Apr 3, 2024

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LAB 4.3 PART 1 Statistics 200: First Lab Activity for Section 4.3 Determining Statistical Significance - Learning objectives:  Recognize that smaller p-values give stronger evidence in support of the alternative hypothesis  Demonstrate an understanding of the concept of statistical significance  Make a formal decision in a hypothesis test by comparing a p-value to the significance level  State the conclusion to a hypothesis test in context  Make a less formal decision that reflects the strength of evidence in a p-value  Conduct a hypothesis test for a variety of situations Activity 1: p-values, evidence for the alternative, and formal decisions. Below are three different hypothesis tests about population proportions. For each test, use StatKey and the information given to calculate the appropriate p-value and make the correct conclusions. 1. H 0 : p = 0.3 vs H a: p ≠ 0.3. A survey used to test these hypotheses found a count of 38 and a sample size of n = 100. a. What is p-hat for this sample? 38/100 = .38 b. Using StatKey, generate a randomization distribution using at least 5000 samples. Remember to: select Edit Data to input sample information, and to edit the null hypothesis. What is the p-value using this randomization distribution? .045 c. What is the formal conclusion using a significance level of 0.05? We can rject H0 d. What is the conclusion in context? We can reject the null hypothesis with evidence that the pvalue Is .045 which is less than 0.05 2. H 0 : p = 0.7 vs H a: p ≠ 0.7. A survey used to test these hypotheses found a count of 320 and a sample size of n = 500. a. What is p-hat for this sample? 320/500 = .64 b. Using StatKey, generate a randomization distribution using at least 5000 samples. Remember to select Edit Data to input sample information, and to edit the null hypothesis. What is the p-value using this randomization distribution? .69 c. What is the formal conclusion using a significance level of 0.05? 12/15/18 © - Pennsylvania State University

LAB 4.3 PART 1 .01 d. What is the conclusion in context? We can reject the hypothesis that p = .7 with a phat of .01 which is less than 0.05 3. H 0 : p = 0.6 vs H a: p < 0.6. A survey used to test these hypotheses found a count of 110 and a sample size of n = 200. a. What is p-hat for this sample? 110/200 = .55 b. Using StatKey, generate a randomization distribution using at least 5000 samples. Remember to select Edit Data to input sample information, and to edit the null hypothesis. What is the p-value using this randomization distribution? .625 c. What is the formal conclusion using a significance level of 0.05? .018 so reject the null What is the conclusion in context? We can reject the hypothesis that p = .6 with a phat of .018 which is less than 0.05 4. Considering your p-values from questions 1 – 3 above, which of the statements below is true ? A. The p-value for Question 2 indicates the most evidence in support of the corresponding alternative hypotheses. B. For Question 1, we accept the null hypothesis at a significance level of 0.05 and of 0.10. C. For Question 2, we would reject the null at a significance level of 0.10, but not at a significance level of 0.05. D. For Question 3, the conclusion would change if it were a two-tailed test when using the same sample statistic. Activity 2: Hypothesis test from start to finish Is there evidence of a negative correlation between systolic blood pressure and heart rate? In a sample of 200 patients, we found a sample correlation of -0.057. 1. State the hypotheses of interest. H0: rho = 0 Ha: rho <0 2. What is the notation and value of the sample statistic? Statistic = r 12/15/18 © - Pennsylvania State University

LAB 4.3 PART 1 3. Use StatKey to generate a randomization distribution for these hypotheses. Use the data set ‘ICU Admissions’ available on StatKey. What is the p-value? .215 4. Which two of the options below are correct interpretations of the p-value (insert your calculated p- value from (3) in the blank): A. If there is no linear association between systolic blood pressure and heart rate in the population, the chance of seeing a sample correlation of -0.057 or less is _______________. B. If there is a negative linear association between systolic blood pressure and heart rate, the chance of seeing a sample correlation of -0.057 or less is _____________. C. If there is no linear association between systolic blood pressure and heart rate in the population, the proportion of samples with a sample correlation of -0.057 or less is _______. D. If there is a negative linear association between systolic blood pressure and heart rate, the proportion of samples with a sample correlation of -0.057 or less is _______________. 5. What is the formal conclusion at a significance level of 0.05? Fail to reject 6. What is the conclusion in context? 7. Based on the p-value you calculated in part 3, what would the correct formal conclusion be if we were testing a two-sided hypothesis with the same sample? A. Reject H 0 and accept Ha B. Reject Ha and accept H 0 C. Fail to reject H 0 D. Fail to reject Ha Activity 3: Hypothesis test from start to finish According to Zillow, the median home price in Canton, OH is 92 thousand dollars. A real estate developer believes that the mean home price is larger. We are to use a sample of n = 10 home sales to see if there is evidence that the mean home price is larger than 92 thousand dollars. The sample mean is 146.8 thousand dollars. 1. State the hypotheses of interest. H0: mu = 92,000 Ha= mu > 92,000 2. What is the notation and value of the sample statistic? x-bar = 146.8 3. Use StatKey to generate a randomization distribution for these hypotheses. Use the data set ‘Home Prices - Canton’. You may need to change the null value. What is the p-value? .032 12/15/18 © - Pennsylvania State University

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LAB 4.3 PART 1 4. Select the option that gives the correct interpretation: The p-value from part 3 gives the chance of seeing a sample mean of ___________ thousand dollars or any value __________ , assuming the population mean home price in Canton, Ohio is truly ________ thousand dollars. A. 146.8, smaller, 92 B. 146.8, larger, 92 C. 92, smaller, 146.8 D. 92, larger, 146.8 5. What is the formal conclusion using a significance level of 0.05? There is sufficient evidence to say the mean is greater than 92,000 6. What is the conclusion in context? 7. What would the p-value and conclusion be if we decided to make the alternative hypothesis two- tailed? 8. Select everything that would result in a p-value larger than that in part 3 above: A. Making the alternative hypothesis two-sided. B. Changing the null value from 92 to 96 C. Changing the null value from 92 to 90 (note – you can do these things in StatKey to see what happens, but you should be able to answer this question without it) 9. Did the sample from Activity 2 or Activity 3 provide more evidence for the corresponding alternative hypothesis? A. Activity 2 B. Activity 3 C. Both Activity 2 and Activity 3 provided the same amount of evidence 12/15/18 © - Pennsylvania State University

Section #04.3.1 shared lab

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