Week 6 practice test 1. - American Public University MATH 302 | COMPLETED

Week 6 practice test 1. - American Public University MATH 302 | COMPLETED 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, μD = μbefore−μafter 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: H0: μD = 0 H1: μD > 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 79 83 61.7 56.8 57.9 44.7 56.8 50.6 71 63.4 80.6 68.9 59.8 33.9 73.1 79 49.9 38.4 59.2 55.4 64.8 55.6 Choose the correct decision, summary and state the p-value.  A. Do not reject H0, there is enough evidence to support the claim that the time to complete the task has decreased when workers are allowed to wear earbuds at work and the p-value = .0012  B. Do not reject H0, there is not enough evidence to support the claim that the time to complete the task has decreased when workers are allowed to wear earbuds at work and the p-value = .0024.  C. Reject H0, there is enough evidence to support the claim that the time to complete the task has decreased when workers are allowed to wear earbuds at work and the p-value = .0024  D. Reject H0, there is enough evidence to support the claim that the time to complete the task has decreased when workers are allowed to wear earbuds at work and the p-value = .0012 Answer Key:D Feedback: Copy and paste the data into Excel. Use the Data Analysis Toolpak in Excel. Data - > Data Analysis -> scroll to where is says t:Test: Paired Two Samples for Means -> OK Variable 1 Range: is Before Variable 2 Range: is After The Hypothesized Mean Difference is 0 and make sure you click Labels in the first row and click OK. You will get an output and this is the p-value you are looking for. P(T<=t) one-tail 0.0012 Question 2 of 20 1.0/ 1.0 Points 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: H0 : μD = 0 H1 : μD > 0 t-Test: Paired Two Sample for Means NonDominant Dominant Mean 63.33 56.28 Variance 218.96431 58 128.75221 05 Observations 20 20 Pearson Correlation 0.9067 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?  A. Do not reject H0  B. Reject H1  C. Accept H0  D. Accept H1  E. Reject H0 Answer Key:E Feedback: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. Part 2 of 7 - Week 6: Comparing Two Independent Population Proportions 2.5/ 3.0 Points Question 3 of 20 1.0/ 1.0 Points TDaP is a booster shot that prevents Diphtheria, Tetanus, and Pertussis in adults and adolescents. It should be administered every 8 years for it to remain effective. A random sample of 500 people living in a town that experienced a pertussis outbreak this year were divided into two groups. Group 1 was made up of 132 individuals who had not had the TDaP booster in the past 8 years, and Group 2 consisted of 368 individuals who had. In Group 1, 15 individuals caught pertussis during the outbreak, and in Group 2, 11 individuals caught pertussis. Is there evidence to suggest that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were? Test at the 0.05 level of significance. Enter the P-Value - round to 4 decimal places. p-value = 0.0001 Answer Key:0.0001|.0001 Feedback: This is an upper tailed test because because of the keyword higher. z = z = 3. Use NORM.S.DIST(3.,TRUE) to find the for the lower tailed test. 0., then 1 - 0., this is the p-value you want to use for an upper tailed test. Question 4 of 20 1.0/ 1.0 Points A high school is running a campaign against the over-use of technology in teens. The committee running the campaign decides to look at the difference in social media usage between teens and adults. They take a random sample of 200 teens in their city (Group 1) and find that 85% of them use social media, and then take another random sample of 180 adults in their city (Group 2) and find that 55% of them use social media. Find a 90% confidence interval for the difference in proportions. Enter the confidence interval - round to 4 decimal places. 0.2262 < p1 - p2 < 0.3738 Answer Key:0.2262|.2262, 0.3738|.3738 Feedback: Z-Critical Value =NORM.S.INV(.95) = 1.645 LL = (.85-.55) - 1.645* UL = (.85-.55) + 1.645* Question 5 of 20 0.5/ 1.0 Points 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. 0.356 < p1 - p2 < 0.139 Answer Key:-0.356|-.356, 0.139|.139 Feedback: Z-Critical Value =NORM.S.INV(.995) = 2.575 LL = (.625-.7333) - 2.575* UL = (.625-.7333) + 2.575* Part 3 of 7 - Hypothesis Testing Questions 3.0/ 5.0 Points Question 6 of