knowledge check 6.1.pdf

1/14/24, 3:34 PM Steven Felmlee - MATH302 D006 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=267645&ai=3059719&isInPopup=0&cfql=0&fromQB=… 1/19 Week 6 Knowledge Check Homework Practice Questio… Attempt 1 of 4 Written Jan 14, 2024 1:16 PM - Jan 14, 2024 3:26 PM Attempt Score 9 / 20 - 45 % Overall Grade (Highest Attempt) 9 / 20 - 45 % Question 1 1 / 1 point A researcher is testing reaction times between the dominant and non-dominant hand. They randomly start with each hand for 20 subjects and their reaction times in milliseconds are recorded. Test to see if the reaction time is faster for the dominant hand using a 5% level of significance. The hypotheses are: H 0 : μ D = 0 H 1 : μ D > 0 t-Test: Paired Two Sample for Means Non-Dominant Dominant Mean 63.33 56.28 Variance 218.9643158 128.7522105 Observations 20 20 Pearson Correlation 0.9067

1/14/24, 3:34 PM Steven Felmlee - MATH302 D006 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=267645&ai=3059719&isInPopup=0&cfql=0&fromQB=… 2/19 Hypothesized Mean Difference 0 df 19 t Stat 4.7951 P(T<=t) one-tail 0.0001 t Critical one-tail 1.7291 P(T<=t) two-tail 0.0001 t Critical two-tail 2.0930 What is the correct decision? Hide ques±on 1 feedback Question 2 1 / 1 point A physician wants to see if there was a difference in the average smokers' daily cigarette consumption after wearing a nicotine patch. The physician set up a study to track daily smoking consumption. In the study, the patients were given a placebo patch that did not contain nicotine for 4 weeks, then a nicotine patch for the following 4 weeks. Test to see if there was a difference in the average smoker's daily cigarette consumption using α = 0.01. The hypotheses are: Accept H 0 Reject H 1 Accept H 1 Do not reject H 0 Reject H 0 The p-value for a one tailed test is 0.0001. This is given to you in the output. No calculations are needed. 0.0001 < .05, Reject Ho, this is significant.

1/14/24, 3:34 PM Steven Felmlee - MATH302 D006 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=267645&ai=3059719&isInPopup=0&cfql=0&fromQB=… 3/19 H 0 : μ D = 0 H 1 : μ D ≠ 0 t-Test: Paired Two Sample for Means Placebo Nicotine Mean 16.75 10.3125 Variance 64.46667 33.29583 Observations 16 16 Pearson Correlation 0.6105 Hypothesized Mean Difference 0 df 15 t Stat 4.0119 P(T<=t) one-tail 0.0006 t Critical one-tail 2.6025 P(T<=t) two-tail 0.0011 t Critical two-tail 2.9467 What is the correct decision? Accept H 0 Do not reject H 0

1/14/24, 3:34 PM Steven Felmlee - MATH302 D006 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=267645&ai=3059719&isInPopup=0&cfql=0&fromQB=… 4/19 Hide ques±on 2 feedback Question 3 0 / 1 point ___ 0.9249___ (0.2958, .2958) Hide ques±on 3 feedback Accept H 1 Reject H 1 Reject H 0 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. A math teacher tells her students that eating a healthy breakfast on a test day will help their brain function and perform well on their test. During finals week, she randomly samples 45 students and asks them at the door what they ate for breakfast. She categorizes 25 students into Group 1 as those who ate a healthy breakfast that morning and 20 students into Group 2 as those who did not. After grading the final, she finds that 48% of the students in Group 1 earned an 80% or higher on the test, and 40% of the students in Group 2 earned an 80% or higher. Can it be concluded that eating a healthy breakfast improves test scores? Use a 0.05 level of significance. Hypotheses: H 0 : p 1 = p 2 H 1 : p 1 > p 2 In this scenario, what is the p-value? (Round to 4 decimal places) p-value = z =

1/14/24, 3:34 PM Steven Felmlee - MATH302 D006 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=267645&ai=3059719&isInPopup=0&cfql=0&fromQB=… 5/19 Question 4 0 / 1 point ___ -0.249___ (-0.356, -.356) ___ 0.166___ (0.139, .139) Hide ques±on 4 feedback z = 0.536656 Use NORM.S.DIST(0.536656,TRUE) to find the for the lower tailed test. 0.704247, then 1 - 0.704247, this is the p-value you want to use for an upper tailed test. Two competing toothpaste brands both claim to produce the best toothpaste for whitening. A dentist randomly samples 48 patients that use Brand A (Group 1) and finds 30 of them are satisfied with the whitening results of the toothpaste. She then randomly samples 45 patients that use Brand B (Group 2) and finds 33 of them are satisfied with the whitening results of the toothpaste. Construct a 99% confidence interval for the difference in proportions and use it to decide if there is a significant difference in the satisfaction level of patients. Enter the confidence interval - round to 3 decimal places. < p 1 - p 2 < Z-Critical Value =NORM.S.INV(.995) = 2.575 LL = (.625-.7333) - 2.575* UL = (.625-.7333) + 2.575*

1/14/24, 3:34 PM Steven Felmlee - MATH302 D006 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=267645&ai=3059719&isInPopup=0&cfql=0&fromQB=… 6/19 Question 5 0 / 1 point In a 2-sample z-test for two proportions, you find the following: p̂ 1 = 0.32 n 1 =50 p̂ 2 = 0.36 n 2 =50 Find the test statistic you will use while executing this test. Hide ques±on 5 feedback Question 6 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: z = -0.42 z = -0.67 z = -1.96 z = ± 1.64 z = 0.34 p = (16+18)/(50+50) = .34 z = two-tailed test one-tailed test, lower tailed test

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