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You should also be using the case overview link as your work on the case. This will explain what section to use from the chapter notes. You must be providing answers to each step in the appropriate section of notes for every test in this case. Question 1 refers to the entire sample of 92 people. 1. A consumer group claims that more than 62% of people choose coffee rather than other beverages as their preferred drink in the morning. In the sample of 92 people, 68 reported that they prefer coffee. Ata = 0.02, is there enough evidence to support the consumer group's claim? You MUST show all 10 steps from the chapter notes in order to receive full credit. (12 points) Questions 2 and 3 refer to the following information regarding the annual consumption of coffee of the 41 males. Of the sample of the 41 males, the sample mean is 25.7 gallons and the sample standard deviation is 3.8 gallons. Assume the data is normally distributed and the sample is randomly selected. 2. Assuming a =0.005, is there enough evidence to support a claim that the mean amount of consumption is at least 28 gallons? You MUST show all 10 steps from the chapter notes in order to receive full credit. (12 points) 3. Assuming a = 0.05, is there enough evidence to support a claim that the standard deviation of the number of servings is 3 gallons? You MUST show all 9 steps from the chapter notes in order to receive full credit. (12 points) Questions 4 & 5 refer to the entire sample of 92 people. 4. For the entire random sample of 92 people, the sample mean is 21.6 gallons. Assume the population standard deviation is 4.8 gallons and that the population is normally distributed. Is there enough evidence to support a claim that the mean amount of consumption is more than 20.2 gallons? Assume a =0.03. You MUST show all & steps from the chapter notes in order to receive full credit. (12 points) 5. Of the 92 people in the sample, the annual consumption of coffee and the weekly amount of hours worked were compared to find r=0.623. Test the significance of this correlation coefficient using a =0.10. Is there a significant correlation between annual coffee consumption and the weekly amount of hours worked? You MUST show all 7 steps from the chapter notes in order to receive full credit. (12 points)
A hypothesis test can be used to determine whether the sample correlation coefficient has enough evidence to conclude that the population correlation coefficient p (rho) is significant As a reminder, the correlation coefficient has a range of values between-1 to with no correlation being 0. The closer the correlation coefficient is to either -1 or 1, then the stronger the correlation is. Hypothesis tests for testing p can be left-tailed, right-tailed, or two-tailed and are based on whether the correlation coefficient is less than, greater than or equal to zero. We will just be focusing on two-tailed tests. How to test the correlation coefficient 1. Identify the null and alternative hypotheses. Since we are only learning the two-tailed test, these two hypotheses will be: Ho: p0 (meaning there is no significant correlation) H.: #0 (meaning there is significant correlation) These hypotheses will not change for any of the correlation coefficient tests we are doing. 2. Specify: Sample correlation coefficient, • Level of significance, a • Sample size, n Degrees of freedom: d.f-n-2 The degrees of freedom for this test are n-2 to account for the two variables that are used in the original calculations of finding the sample correlation coefficient 3. Determine the critical values in table 5 on the t-distribution. Lookup the degrees of freedom and the level of significance in the two tail row on the table. • You should be identifying two critical values since you have a two tailed test. One critical value is the positive value from the table and the other is the negative value. You need to state both. 4. Identify the rejection regions and show them on a sketch of the normal distribution The rejection regions would be the shaded regions on the graph, which are the left tail and the right tail. 5. Find the standardized test statistic: 6. Make a decision to reject or fail to reject the null hypothesis. • Reject Hoift (the standardized test statistic from step 5) is in the rejection region. • Fail to reject He ift is not in the rejection region. 7. Interpret the decision by indicating whether there is significant correlation or not. There is significant correlation if you are rejecting Ho. There is no significant correlation if you are failing to reject Ho.
Example 1: The ages in years of 11 children and the number of words in their vocabulary were compared to find r=0.996. Test the significance of this correlation coefficient. Use a =0.05. Step 1: Ho: p=0 (meaning there is no significant correlation) H:p #0 (meaning there is significant correlation) Step 2:r=0.996 q=0.05 d.f.-11-29 Step 3: Critical values --2.262 and 2.262 Step 4: Rejection regions: <-2.262 and t> 2.262 2.202 0.996 Step 5:1 33.440 Step 6: Reject He sincet is in the rejection region. Step 7: If we are rejecting the null then we are failing to reject the alternative. This means there is significant correlation between the age and number of words in vocabulary of children. Example 2: The salaries and average attendances at home games for the 30 teams in Major League Baseball in 2012 were compared to find r=0.769. Test the significance of this correlation coefficient. Use a =0.01. Step 1: Ho: p=0 (meaning there is no significant correlation) H: P+0 (meaning there is significant correlation) Step 2:r=0.769 a=0,01 n = 30 d.f. - 30-2 = 28 Step 3: Critical values -2.763 and 2.763 Step 4: Rejection regions: 1 <-2.763 and t > 2.763 2.703 2.709 Step 5:1 0.769 1-0.7692 28 6.366 Step 6: Reject Hosincet is in the rejection region. Step 7: If we are rejecting the null then we are failing to reject the alternative. This means there is significant correlation between the salaries and average attendance.