The 2019-20 season is Lebron James’s 17th season in league. Most players are past their peak at this career stage, and so some have predicted that Lebron’s performance will decline. Last season, Lebron’s average points per game was 27.4. In the first 9 games of this season, his average points per game was 24.6 with a standard deviation of 8.0. Conduct a hypothesis test to test this prediction using α=0.1 as the significance level. Step 1: State the null and alternative hypotheses.   Step 2: Choose the significance level. Step 3: Calculate the test statistic.   Step 4: Find the critical value(s). Step 5: Compare the test statistic to the critical value(s).   Step 6: State the conclusion.

Customers arrive on average every 30 minutes to The Grease Monkey, an auto repair shop with only one mechanic. The inter-arrival times are exponentially distributed. Repair times are variable with a mean of 25 minutes and a standard deviation of 20 minutes. The mechanic works on one vehicle at a time from beginning to end and takes in any waiting vehicles on a first-come first-served basis. The garage itself has room for only one vehicle at a time, so waiting vehicles are kept in the parking lot where there are always plenty of spaces available. Assume customers never balk or renege. a)What is the average number of cars in the garage (not including the parking lot)? b) How long (in minutes) do vehicles wait on average in the adjacent parking lot? c) The competitor shop across the street also has a single mechanic and an average of 3.1 vehicles waiting in its parking lot. The competitor only does oil changes, which take an average of 21 minutes. Customer inter-arrival times to the…

In the year 2033, katy perry is a leading traveling nurse. Katy is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Katy takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. g) What is the interpretation (not your conclusions) of the p value in the context of the problem you found in part e? h) What are your conclusions in the context of the problem? Relate your conclusions to the test statistic and critical value, confidence interval and p value.

A dean in the business school claims that GMAT scores of applicants to the school's MBA program have increased during the past 5 years. Five years ago, the mean and standard deviation of GMAT scores of MBA applicants were 550 and 60, respectively. 30 applications for this year's program were randomly selected and the GMAT scores recorded. If we assume that the distribution of GMAT scores of this year's applicants is the same as that of 5 years ago, find the probability of erroneously concluding that there is not enough evidence to supports the claim when, in fact, the true mean GMAT score is 590. Assume αα is 0.02.

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 36 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes is normal.

A lightbulb is warranted to last for 5,000 hours. If the time to failure is exponentially distributed with a true mean of 4,800 hours, what is the probability that it will last at least 5,000 hours?

The human resources department of a consulting firm gives a standard creativity test to a randomly selected group of new hires every year. This year, 65 new hires took the test and scored a mean of 113.2 points with a standard deviation of 13.4. Last year, 100 new hires took the test and scored a mean of 116.8 standard deviation of 14.6. Assume that the population standard deviations of the test scores of all new hires in the current year and the test scores of all new hires last year can be estimated by the sample standard deviations, as the samples used were quite large. Construct a 95% confidence interval points with for 4-, the difference between the mean test score u, of new hires from the current year and the mean test score , of new hires from last year. Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places. (If necessary, consult a list of…