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 4 workers' times were collected with and without earbuds. Assume the populations of time to complete the task is normal. Without earbuds With earbuds 36.7 34 51.9 49.5 43.4 42 46.8 43.6 Test whether the time to complete the task changed, on average, with earbuds at a significance level of a = 0.05. The test statistic is (use 4 decimal places)

A consumer magazine wants to compare the lifetimes of ballpoint pens of three different brands (measured in days). The magazine takes a random sample of pens of each type in the following table. What is the correct test statistic? Brand 1 Brand 2 Brand 3 382 181 238 242 140 257 216 162 241 319 218 213 a. F (2, 9) = 5.54 b.r = -.34 c. t (11) = 12.16 d.p = .027

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…

Julius has conducted a very small study of the amount of sleep his dorm mates get each night. He believes that those who are on one of the school’s sports teams will get more sleep (measured in hours per night) than those who are not. Julius surveyed 12 people. Of these, 6 played on a sports team and 6 did not. The descriptive statistics from his survey are given below. PLAYS SPORTS (Sample 1) DOES NOT PLAY SPORTS (Sample 2) 8 6 9 6 8 5 7 7 8 7 7 6 What is the critical value for this test? what is the t-obtain value for this t-test? Based on your t-obtained value, what should you conclude about the null hypothesis for this test?

A hypertension trial is mounted, and 12 participants are randomly assigned to receive either a new medication or a placebo. Each participant takes the assigned medication, and the participants’ SBP is recorded after 6 months on the assigned medication. The data are shown in Table 7–9. Is there a difference in mean SBP between treatments? Run the appropriate test at a = 0.05. Placebo New Medication 134 114 143 117 148 121 142 124 150 122 160 128

The mean number of sick days an employee takes per year is believed to be about 10.5. Members of a personnel department do not believe this figure. They randomly survey ten employees. The number of sick days they took for the past year are as follows: 12; 4; 15; 3; 11; 8; 6; 8; 2; 9. Let x = the number of sick days they took for the past year. Should the personnel team believe that the mean number is ten?

The city of Hampton is surveying households to see if the number of cats per household has changed over the past decade. The last known average of cats per household was 1.08. What statistical procedure should you use to analyze these data? O one sample z test Oone sample t test O correlated groups t test O independent groups t test

During the month of January 2017, a total of 29,404 flights took off from a particular airport. Of all these flights, 23.9 % had a departure delay of more than 10 minutes. Suppose we randomly sample just 100 of these flights. Complete parts a through d. a. What sample proportion should we expect to see in such a sample, and how much should we expect the proportion to vary from sample to sample in samples of size 100? The mean is (Round to three decimal places as needed.)