A manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task will change when they are allowed to wear ear buds at work. A random sample of 21 workers' times were collected before and after. Test the claim that the time to complete the task has changed at a significance level of a = 0.05. For the context of this problem, Ha = Hafter - Hbef or e where the first data set represents after and the second data set represents before. Assume the population is normally distributed. Round answers to 4 decimal places. H.: Ha = 0 Ha: Hd + 0 You obtain the following sample of data: Before 53.5 52.9 After 64.4 45.4 51.7 58.4 52.4 55.5 58.2 35.9 75.5 21.4 40.7 48.6 60.5 52.4 26.8 51.5 38.2 44.2 53.3 55.7 38.7 53.5 25.5 52.8 49.4 50.5 19,9 48.8 41.3 50.3 38.8 47 62 53.1 51.7 52.6 23.1 49.5 49.8 49.7 What is the critical value for this test? critical value = +| What is the test statistic for this sample? test statistic - The test statistic is... Select an answer This test statistic leads to a decision to... Select an answer As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the time to complete the task has changed. O There is not sufficient sample evidence to support the claim that the time to complete the task has changed. O There is not sufficient evidence to warrant rejection of the claim that the time to complete the task has changed. O The sample data support the claim that the time to complete the task has changed.

A hypertension trial is mounted and 12 participants are randomly assigned to receive either a new treatment or a placebo.  Each participant takes the assigned medication and their systolic blood pressure (SBP) is recorded after 6 months on the assigned treatment.  The data are as follows.   Placebo New Treatment 132 114 143 119 148 121 144 124 155 126 160 128  Is there a difference in mean SBP between treatments? Run the test at a 5% level of significance. Give each of the following to receive full credit : 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic ; and 5) your conclusion including a comparison to alpha or the critical value. You MUST show your work to receive full credit. Partial credit is available.

An auditor for a local court system is tasked with comparing the rulings of two judges. The auditor needs to determine if Judge Hughes issues shorter sentences than Judge Wilson. The data below are the sentence lengths, in months, issued by each judge in their last twelve cases that dealt with operating a motor vehicle without a license. Test the claim that Judge Hughes issues shorter sentences than Judge Wilson for this particular type of case at the 0.05 level of significance. Let Judge Hughes' sentences be Population 1 and let Judge Wilson's sentences be Population 2. Assume that both populations are approximately normal and that the population variances are equal. Judge 24 12 12 30 Hughes 36 30 12 18 24 12 24 30 Judge 36 36 24 24 24 24 18 12 30 24 18 30 Wilson Copy Data Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.

The mean number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do not believe this figure. They randomly survey 8 employees. The number of sick days they took for the past year are as follows: 10; 5; 13; 3; 11; 8; 6; 9. Let X = the number of sick days they took for the past year. Should the personnel team believe that the mean number is about 10? Conduct a hypothesis test at the 5% level.Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)   t  =    Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence…