An important problem in industry is shipment damage. A electronics distribution company ships its product by truck and determines that it can meet its profit expectations if, on average, the number of damaged items per truckload is fewer than 12. A random sample of 12 departing truckloads is selected at the delivery point and the average number of damaged items per truckload is calculated to be 11.3 with a calculated sample of variance of 0.49. Select a 95% confidence interval for the true mean of damaged items.

A light bulb manufacturer wants to compare the mean lifetimes of two of its light bulbs, model A and model B. Independent random samples of the two models were taken. Analysis of 10 bulbs of model A showed a mean lifetime of 1347 hours and a standard deviation of 92 hours. Analysis of 13 bulbs of model B showed a mean lifetime of 1380 hours and a standard deviation of 111 hours. Assume that the populations of lifetimes for each model are normally distributed and that the variances of these populations are equal. Construct a 95% confidence interval for the difference −μ1μ2 between the mean lifetime μ1 of model A bulbs and the mean lifetime μ2 of model B bulbs. 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 responses to at least two decimal places. Upper Limit Lower Limit:

A large financial company employs a human resources mamanger who is in charge of employe benefits. The manger wishes to estimate the average dental expenses per employee for the company. She selects a random sample of 60 employee records for the past year and determines that the sample mean of $492. Moreover, it is known from past studies that the population standard deviation for annual dental expenses is $74. Use this data to calculate a 95% cofidence interval for the mean expenses of all employees.

A large p-value indicates that the data is consistent with the alternative hypothesis.   True or false?

An instructor has decided to introduce a greater component of independent study into an intermediate microeconomics course as a way of motivating students to work independently and think more carefully about the course material. A colleague cautions that a possible consequence may be increased variability in student performance. However, the instructor responds that she would expect less variability. From her records she found that in the past, student scores on the final exam for this course followed a normal distribution with standard deviation 18.2 points. For a class of 25 students using the new approach, the standard deviation of scores on the final exam was 15.3 points. Assuming that these 25 students can be viewed as a random sample of all those who might be subjected to the new approach, test the null hypothesis that the population standard deviation is at least 18.2 points against the alternative that it is lower.

An intercity bus company is attempting to improve the reliability of its service.  One manager claims that the variability (i.e., standard deviation) in arrivals from the posted schedule at the central bus depot is approximately 3 minutes.  Another manager disagrees, suspecting that the spread in times of arrival is different.  Using variance, what is the population parameter under consideration?  What hypotheses should the managers test in this situation?

Suppose a researcher pbserves a population of 12 people and computes SS=204. What is the variance? What is the standard deviation?

A basketball coach believes that the variance of the heights of adult male basketball players is different from the variance of heights for the general population of men. The sample variance of heights, measured in inches, for a random sample of 19 basketball players is 14.22. The sample variance for a random sample of 18 other men is 34.49. Assume that both population distributions are approximately normal and test the coach’s claim using a 0.10 level of significance. Does the evidence support the coach’s claim? Let male basketball players be Population 1 and men in general be Population 2.   Step 1 of 3:  State the null and alternative hypotheses for the test. Fill in the blank below. H0: σ21=σ22: Ha: σ21⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯σ22 Step 2 of 3:  Compute the value of the test statistic. Round your answer to four decimal places. Step 3 of 3:  Draw a conclusion and interpret the decision.

In one city, the average amount of time that tenth-graders spend watching television each week is 23 hours. The principal of Birchwood High School believes it is less for the 10th grade students that at his school.  For a sample of 95 tenth-graders from the school, the mean amount of time spent watching television per week was 21.9 hours.  Assuming a population standard deviation of 3.1 hours, does the data provide sufficient evidence to conclude that for all tenth-graders at Birchwood High school, the mean amount of time spent watching television per week is less than the city average of 23 hours?  Perform the appropriate hypothesis test using a significance level of 0.005.  What are the hypotheses?         What is the test statistic? Is it a z or a t?         Find the P-value for this test statistic. How does it compare to the significance level?  On the normal curve, indicate the location of the test statistic  and  the p-value. (label them on the graph)                 Write…

An automobile manufacturer has given its van a 50.6 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 220 vans, they found a mean MPG of 50.5. Assume the population variance is known to be 1.69. A level of significance of 0.01 will be used. Find the P-value of the test statistic. you may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.