Directions: Complete each of the following problems. Be sure to show your work in order to receive full or partial credit. You may use your book or class notes to complete this quiz however; you are not to talk to your classmates, peers, family, or other teachers to get help on this quiz. Please direct all questions to Dr. Manzanares. 1. It is believed that 25% of US. homes have a direct satellite television receiver. How large of a sample is necessary to estimate the true population of homes that do have direct satellite television receivers with 95% condence and within 3 percentage points? (3 points) 2. A meteorologist who sampled 13 randomly selected thunderstorms, found that the average speed at which they traveled across a certain state was 15.0 miles per hour. The standard deviation of the sample was 1.7 miles per hour. a. Find the 99% condence interval of the mean. (3 points) b. Interpret this interval in the context of this problem. (1 point) 3. Consider the following scenario and determine the p-value or p-value interval. (2 points) a. t= 2.409, n=30, two-tailed h. 2 =1.86, right tailed 4. Consider the following P-values, critical values, or test values and determine if you would reject H0 or fail to reject Ho. Justify your decision. (2 points) a. Critical Value = i2.183 and a test value of -2.191 b. p=0.0201 a=0.02 5. The Dean of the College of Liberal Arts and Sciences (CLAS) reported that the mean time for CLAS students to complete their degree at CU-Denver is less than 5 years. She randomly selected 81 recent CLAS graduates and found that the mean time to graduate was 4. 70 years with a standard deviation of 1.21 years. At a = 0.01 is the Dean's claim correct? (6 points) a. State the hypotheses and identify the claim. b. Find the critical value. c. Compute the test value. 6. A corrections ofcer read that 58% of runaways are female. He believes that the percentage is higher than 53%. He selected a random sample of 90 runaways and found that 6] were female. An (1 = 0.05, can you conclude that his belief is correct? (8 points) a. State the hypotheses and identify the claim. b. Compute the test value. c. Find the p-value. (1. Make the decision to reject or not reject the null hypothesis. Justify. e. Summarize the results