Quizzes - MATH302 WK6 Homework

12/19/23, 1:48 PM Kimberly Mioducki - MATH302 I010 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/attempt/quiz_start_frame_auto.d2l?ou=139305&isprv=&qi=260783&cfql=0&dnb=0&fromQB=0&i… 3/19 Hide ques±on 1 feedback Question 2 1 / 1 point A manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task is faster if they are wearing earbuds. A random sample of 20 workers' times were collected before and after wearing earbuds. Test the claim that the time to complete the task will be faster, i.e. meaning has production increased, at a significance level of α = 0.01 For the context of this problem, μ D = μ before −μ after where the first data set represents before earbuds and the second data set represents the after earbuds. Assume the population is normally distributed. The hypotheses are: H 0 : μ D = 0 H 1 : μ D > 0 You obtain the following sample data: Before After 68 62.3 72.5 61.6 39.3 21.4 67.7 60.4 38.3 47.9 85.9 78.6 67.3 75.1 59.8 48.3 72.1 65 Reject H 0 Accept H 1 The p-value for a two tailed test is 0.0011. This is given to you in the output. No calculations are needed. 0.0011 < .01, Reject Ho, this is significant.

12/19/23, 1:48 PM Kimberly Mioducki - MATH302 I010 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/attempt/quiz_start_frame_auto.d2l?ou=139305&isprv=&qi=260783&cfql=0&dnb=0&fromQB=0&i… 6/19 Question 4 1 / 1 point A researcher took a random sample of 200 new mothers in the United States (Group 1) and found that 16% of them experienced some form of postpartum depression. Another random sample of 200 new mothers in France (Group 2), where mothers receive 16 weeks of paid maternity leave, found that 11% experienced some form of postpartum depression. Can it be concluded that the percent of women in the United States experience more postpartum depression than the percent of women in France? Use α=0.05 . Select the correct alternative hypothesis and decision . Hide ques±on 4 feedback H 1 : p 1 ≠ p 2 ; Do not reject the null hypothesis. H 1 : p 1 ≠ p 2 ; Reject the null hypothesis. H 1 : p 1 > p 2 ; Do not reject the null hypothesis. H 1 : p 1 > p 2 ; Reject the null hypothesis. H 1 : p 1 < p 2 ; Do not reject the null hypothesis. H 1 : p 1 < p 2 ; Reject the null hypothesis. This is an upper tailed test because because of the keyword more. z = z = 1.463171 Use NORM.S.DIST(1.463171,TRUE) to find the for the lower tailed test. 0.92829, then 1 - 0.92829, this is the p-value you want to use for an upper tailed test.

12/19/23, 1:48 PM Kimberly Mioducki - MATH302 I010 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/attempt/quiz_start_frame_auto.d2l?ou=139305&isprv=&qi=260783&cfql=0&dnb=0&fromQB=0&i… 9/19 Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 7.7 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer than 7.7 seconds. What would you use for the alternative hypothesis? Hide ques±on 9 feedback Question 10 1 / 1 point If a teacher is trying to prove that a new method of teaching economics is more effective than a traditional one, he/she will conduct a: Hide ques±on 10 feedback H 1 : < 7.7 seconds H 1 : = 7.7 seconds H 1 : ≥ 7.7 seconds H 1 : > 7.7 seconds Hypothesized value is 7.7 and this is an upper tailed test because of the keyword longer. one-tailed test, lower tailed test point estimate of the population parameter two-tailed test a one tailed, upper tailed test Upper tailed test because the keyword is more.

12/19/23, 1:48 PM Kimberly Mioducki - MATH302 I010 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/attempt/quiz_start_frame_auto.d2l?ou=139305&isprv=&qi=260783&cfql=0&dnb=0&fromQB=0… 12/19 Question 13 0 / 1 point A new over-the-counter medicine to treat a sore throat is to be tested for effectiveness. The makers of the medicine take two random samples of 25 individuals showing symptoms of a sore throat. Group 1 receives the new medicine and Group 2 receives a placebo. After a few days on the medicine, each group is interviewed and asked how they would rate their comfort level 1-10 (1 being the most uncomfortable and 10 being no discomfort at all). The results are below. Find the 95% confidence interval in the difference of the mean comfort level. Is there sufficient evidence to conclude that the new medicine is effective? Assume the data is normally distributed with unequal variances. (Round answers to 4 decimal places) Make sure you put the 0 in front of the decimal. Average Group 1 = 5.84, SD Group 1 = 2.211334, n1 = 25 Average Group 2 = 3.96, SD Group 2 = 2.35372, n2 = 25 ___< μ 1 - μ 2 <___ ___ Answer for blank # 1: 0.7967 (0.5813, 0.5812) Answer for blank # 2: 2.9634 (3.1787, 3.1788) Hide ques±on 13 feedback T-Critical Value =T.INV.2T(.05,48) = 2.010635 LL = (5.84 - 3.96) - 2.010635 * UL = (5.84 - 3.96) + 2.010635 *

12/19/23, 1:48 PM Kimberly Mioducki - MATH302 I010 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/attempt/quiz_start_frame_auto.d2l?ou=139305&isprv=&qi=260783&cfql=0&dnb=0&fromQB=0… 15/19 Question 15 0 / 1 point Which of the following is a requirement that must be true in order to run a t- test over a z-test? Question 16 0 / 1 point In a random sample of 50 Americans five years ago (Group 1), the average credit card debt was $5,798. In a random sample of 50 Americans in the present day (Group 2), the average credit card debt is $6,511. Let the population standard deviation be $1,154 five years ago, and let the current population standard deviation be $1,645. Using a 0.01 level of significance, test if there is a difference in credit card debt today versus five years ago. What are the correct hypotheses for this problem? Make sure you click Labels in the first row and click OK. You will get an output and this is the one tailed p-value you are looking for. 0.0021 The standard deviations for both populations must be known. The standard deviations should come from each sample. If the sample sizes are less than 30, the populations need to be approximately normal. The populations must be approximately normal. H 0 : μ 1 = μ 2 ; H 1 : μ 1 ≠ μ 2 H 0 : μ 1 ≤ μ 2 ; H 1 : μ 1 ≥ μ 2 H 0 : μ 1 ≠ μ 2 ; H 1 : μ 1 = μ 2 H 0 : μ 1 ≥ μ 2 ; H 1 : μ 1 ≤ μ 2 H 0 : μ 1 = μ 2 ; H 1 : μ 1 > μ 2 H 0 : μ 1 < μ 2 ; H 1 : μ 1 = μ 2

12/19/23, 1:48 PM Kimberly Mioducki - MATH302 I010 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/attempt/quiz_start_frame_auto.d2l?ou=139305&isprv=&qi=260783&cfql=0&dnb=0&fromQB=0… 18/19 What is a type I error in the context of this problem? Question 20 1 / 1 point A student is interested in becoming an actuary. They know that becoming an actuary takes a lot of schooling and will have to take out student loans. They want to make sure the starting salary will be higher than $55,000/year. They randomly sample 30 starting salaries for actuaries and find a p-value of 0.0392. Use α = 0.05. Should the student pursue an actuary career? Hide ques±on 20 feedback Done The corporation will not market the Stumptown Berry even though the berry does produce fruit within the 90 days. The corporation will market the Stumptown Berry even though the berry does produce fruit in more than 90 days. The corporation will not market the Stumptown Berry even though the berry does produce fruit in more than 90 days. The corporation will market the Stumptown Berry even though the berry does produce fruit within the 90 days. No, since we reject the claim. Yes, since we reject the claim. No, since we reject the null hypothesis. Yes, since we reject the null hypothesis. Yes, the p-value is < .05 and we Reject Ho and this is significant.