Question

Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 36 hours and a standard deviation of 5.8 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 16 batteries. (20 pts) What can you say about the shape of the distribution of the sample mean? Why? What is the standard error of the distribution of the sample mean? What proportion of the samples will have a mean useful life of more than 38 hour? What proportion of the sample will have a mean useful life greater than 35.5 hours? What proportion of the sample will have a mean useful life between 35.5 and 38 hours?

Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 6,050 pounds and the standard deviation is 320 pounds. Assume that the population follows the normal distribution. Fifty-five trucks are randomly selected and weighed. Within what limits will 99 percent of the sample means occur? (20 pts)

A sample of 230 observations is selected from a normal population with a population standard deviation of 26. The sample mean is 18. (20 pts) Determine the standard error of the mean. Determine the 98% confidence interval for the population mean.

Suppose the U.S. president wants to estimate the proportion of the population that supports his current policy toward revisions in the health care system. The president wants the estimate to be within 0.03 of the true proportion. Assume a 98% level of confidence. The president’s political advisors found a similar survey from two years ago that reported that 58% of people supported health care revisions. (20 pts) How large of a sample is required? How large of a sample would be necessary if no estimate were available for the proportion supporting current policy?

A sample of 38 observations is selected from a normal population. The sample mean is 47, and the population standard deviation is 7. Conduct the following test of hypothesis using the 0.05 significance level. H0: μ = 48; H1: μ ≠ 48      (20 pts) Is this a one- or two-tailed test What is the decision rule? What is the value of the test statistic? What is your decision regarding H0?

Answer 1

(1).(a) The shape of the distribution of the sample mean tend to be normal Reason: The distribution of sample means is defined as the set of means from all the possible random samples of a specific size selected from a specific population. SE = =1.45 The value of the standard error of the distribution of the sample mean is 1.45.

P(X > 38) 1-P(I <38) =1-P(Z 51.38) =1-0.9162 =0.0838 Thus the proportion of the samples will have a mean useful life of more than 38 hour is 0.0838. (d) P(x > 35.5)=1-PCA S 35.5) =1-P(Z <-0.34) =1-0.3669 = 0.6331

Thus the proportion of the sample will have a mean useful life greater than 35.5 hours is 0.6331. P(35.5<7<38) = P(<38) - P(7 335.5) EPI-438-368-4 35.5- = P(Z <1.38) - P(Z 3-0.34) =0.9162-0.3669 =0.5493 Thus the proportion of the sample will have a mean useful life between 35.5 and 38 hours is 0.5493.