The admitting office at Sisters of Mercy Hospital wants to be able to inform patients of the average level of expenses they can expect per day. Historically, the average has been approximately $1270. The office would like to know if there is evidence of a decrease in the average daily billing. Seventy-four randomly selected patients have an average daily charge of $1208 with a standard deviation of $234. Conduct a hypothesis test to determine whether there is evidence that average daily charges have decreased at a significance level of α=0.05. Assume the population of daily hospital charges is approximately normally distributed.
a.
State the null and alternative hypotheses for the test. Fill in the blank below.
H0Ha: μ=1270: μb ? 1270
b. Compute the value of the test statistic. Round your answer to three decimal places.
c. Draw a conclusion and interpret the decision.

A hospital director believes that above 77% of the test tubes contain errors and feels an audit is required. A sample of 200 tubes found 160 errors. Is there sufficient evidence at the 0.01 level to substantiate the hospital director's claim?
State the null and alternative hypotheses for the above scenario.

Determine the critical values for the confidence interval for the population standard deviation from the given values. Round your answers to three decimal places.
n=3 and α=0.2.

A quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective. Suppose a sample of 609 floppy disks is drawn. Of these disks, 536 were not defective. Using the data, estimate the proportion of disks which are defective. Enter your answer as a fraction or a decimal number rounded to three decimal places.
b. Using the data, construct the 90% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places.

A manufacturer of automobile batteries is concerned about the life of the batteries that are produced. The manufacturer is comfortable with the average life of the batteries but more concerned about the standard deviation. Research has shown that the average life of the automobile batteries is 55 months. However, the manufacturer would like the standard deviation of the life of the automobile batteries to be relatively small, say, approximately nine months. To determine a reliable range of the standard deviation of the batteries currently being produced, the manufacturer took a random sample of 20 batteries and found that the average life was 58 months with a standard deviation of eight months. Assuming that the life of batteries produced by the automobile manufacturer has an approximately normal distribution, construct an 80% confidence interval for the standard deviation of the life of their automobile batteries. Round any intermediate calculations to no less than six decimal places and round the endpoints of the interval to four decimal places.