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Pennsylvania State University *

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Statistics

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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
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