A computer manufacturer estimates that its line of minicomputers has, on average, 8.2 days of downtime per year. To test this claim, a researcher contacts seven companies that own one of these computers and is allowed to access company computer records. It is determined that, for the sample, the average number of downtime days is 5.7, with a sample standard deviation of 1.4 days. Assuming that number of downtime days is normally distributed, test to determine whether these minicomputers actually average 8.2 days of downtime in the entire population. Let α = .01. (Round your answer to 2 decimal places.)

1. A random sample of 30 warehouses was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) was recorded for each warehouse in the sample for the March quarter of 2019. The average usage was found to be 375kWh. In a very large study in the March quarter of the previous year it was found that the standard deviation of the usage was 81kWh. Assuming the standard deviation is unchanged and that the usage is normally distributed, calculate a 99% confidence interval for the mean usage in the March quarter of 2019.

In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 38 and a standard deviation of 8. Using the Standard Deviation Rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 30 and 46?

An engineer working for a tire manufacturer investigates the average life of a new material to be used in the manufacturing process. For this purpose, he builds a sample of 13 tires and tests them in a laboratory until the end of their useful life is reached. The data obtained from the sample are as follows: average of 60897.9 km and standard deviation of 2734.8 km. The engineer would like to demonstrate that the average service life of the tire with the new material exceeds 60,000 km. a) State the null and alternative hypothesis to be stated in this experiment. Test the stated hypotheses using an α = 0.05 What conclusions are reached? b) Find a 95% confidence interval for the average tire life with the new material. Interpret your answer.   (RESPOND MANUALLY) (RESPOND MANUALLY)

A very large company is interested in its employees' productivity. The company reports from its historical data that its employees spend a mean of 164 minutes per employee (on a typical day) dealing with email. To test this claim, an independent consultant chooses 26 employees at random and finds that those employees spend a sample mean of 172 minutes dealing with email, with a sample standard deviation of 21 minutes. Assume that the population of amounts of time employees spend dealing with email is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to reject the claim that u, the mean number of minutes employees spend dealing with email, is equal to 164. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test. Ho: I H: OSO D=D (b) Perform at test and find the p-value. Here is some information to help you with your t test.

A district councilor informs the prospective developer of a shopping centre that the average monthly income per household in his district is 2500 Great Britain Pound. Suppose that the household income in the district is approximately normally distributed and that the standard deviation is about 200 Great Britain Pound, based on an earlier study. For a random sample of 25 households, the mean household income is found to be 2400 Great Britain Pound. At a 5% level of significance, can we justify the district councilor’s claim? If not, at what significance level we can justify?

Pandemic-fueled challenges forced consumers to wait significantly longer in drive-thru lanes. QSR magazine studied drive-thru times for 10  fast-food restaurants the lengths of time customers would spend in the drive-thru lane – and found that KFC  in 2020, had the shortest mean time with a mean time spent in the drive-through lane of 283.3 seconds. Assuming drive-through times are Normally distributed with a standard deviation of 33 seconds, answer the following.     a. What percentage of drive-through times at KFC will last more than 300 seconds?  b. The longest 10% of drive-through times are longer than how many seconds?  round top the nearest second.  c. If we select a customer in the drive-through lane at KFC at random, what is the probability that their drive-through time is between 275 and 290 seconds?    d. Dring Lunchtime, it is estimated that 230 customers go through the drive-thru, how many customers have to wait for less than 305 seconds.