A tech company claims that their new software reduces the average time taken to process a specific task by 2 minutes compared to the existing software in the market. An independent tech reviewer wants to test this claim. They conduct an experiment with 40 users. Half of them use the new software, and the other half use the existing software. The differences in processing times (new software - existing software) are recorded for each user. The sample mean difference is found to be 1.5 minutes with a standard deviation of 1.2 minutes. Test the company's claim at a 1% significance level.

A manager evaluates effectiveness of a major hardware upgrade by running a certain process 40 times before the upgrade and 40 times after it. Based on these data, the average running time is 8.6 minutes before the upgrade, 7.3 minutes after it. Historically, the standard deviation has been 1.8 minutes, and presumably it has not changed. Construct a 90% confidence interval showing how much the mean running time reduced due to the hardware upgrade.

A study was conducted to estimate μ, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be σ = 3.6 hours.A similar study conducted a year earlier estimated that μ, the mean number of weekly hours that U.S. adults use computers at home, was 8 hours. We would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean has changed since the previous year.Using a 95% confidence interval of (7.7, 9.3), which of the following is an appropriate conclusion? The current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval. The current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval. The current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval. The current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval. You cannot draw a conclusion because the only way to reach a conclusion is to find the p-value of the test.

The manager of a grocery store has taken a random sample of 100 customers to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. She observes that the average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes.

An analyst has timed a metal-cutting task for 50 cycles. The average time per cycle was 11.9 minutes, and the standard deviation was 1.32 minutes for a worker with a performance rating of 130 percent. Assume an allowance of 17 percent of task time. Calculate the standard time for this task. (Do not round intermediate calculations. Round the final answer to 2 decimal places.)

A company decided to test the hypothesis that the average time a company’s employees are spending to check their private e-mails at work is more than 9 minutes. A random sample of 50 employees were selected and they averaged 9.6 minutes. It is believed that the population standard deviation is 2.5 minutes. The α is set to 0.05. The p-value for this hypothesis test would be __________.