Statistics 200_ First Lab Activity for Section 4.3

Statistics 200: First Lab Activity for Section 4.3 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? a. 0.38 a. 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? 0.0 a. What is the formal conclusion using a significance level of 0.05? a. Reject b. What is the conclusion in context? a. At a significance level of 0.05, we can reject the null hypothesis that p=0.3 1. 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? a. 0.64 a. 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? 0.03 a. What is the formal conclusion using a significance level of 0.05? a. Reject b. What is the conclusion in context? a. At a significance level of 0.05, there is significant evidence to reject the null hypothesis of p=0.7 1. 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? a. 0.55 a. 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? - 0.03 a. What is the formal conclusion using a significance level of 0.05? a. Reject b. What is the conclusion in context? a. At a significance level of 0.05, there is significant evidence to reject the null hypothesis of p=0.6

1. 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. a. Ho: p = 0 b. Ha: p < 0 1. What is the notation and value of the sample statistic? a. Notation = r b. Value = -0.057 1. Use StatKey to generate a randomization distribution for these hypotheses. Use the data set ‘ICU Admissions’ available on StatKey. What is the p-value? - 0.213 1. 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 _______________. 1. What is the formal conclusion at a significance level of 0.05? a. Fail to reject 1. What is the conclusion in context? a. There is not evidence to support the idea that it could be a negative correlation 1. 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