Concept explainers
Exercise 8.58 stated that a random sample of 500 measurements on the length of stay in hospitals had sample
8.58 The administrators for a hospital wished to estimate the average number of days required for inpatient treatment of patients between the ages of 25 and 34. A random sample of 500 hospital patients between these ages produced a mean and standard deviation equal to 5.4 and 3.1 days, respectively. Construct a 95% confidence interval for the mean length of stay for the population of patients from which the sample was drawn.
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Chapter 10 Solutions
Mathematical Statistics with Applications
- To test whether or not there is a significant difference in the average snowfall in Maryland, and Virginia, the average snowfall in the two states during a random sample of 92 days during a leap year were recorded. In Maryland, the average is 5.4 inches with a standard deviation of 0.4 inches and in Virginia, the average is 5.2 inches with a standard deviation of 0.4 inches. Test the hypothesis at a 10% level of significance. Use the F-test to solve the Behrens Fisher problem, use Welsh's approximation, the Wilson Hilferty approximation. Use the p-value method. View keyboard shortcutsarrow_forwardSample surveys conducted in a large county in a cer-tain year and again 20 years later showed that originally the average height of 400 ten-year-old boys was 53.8inches with a standard deviation of 2.4 inches, whereas20 years later the average height of 500 ten-year-old boyswas 54.5 inches with a standard deviation of 2.5 inches.Use the four steps in the initial part of Section 1 andthe 0.05 level of significance to test the null hypothesisμ1 − μ2 = −0.5 against the alternative hypothesis μ1 −μ2 < −0.5.arrow_forwardAckerman and Goldsmite found that students who studed tesxt from printed hardcopy had better test scores than students who studied from text presented on a screen. In a related study, a professor noticed that several students in a large class had purchased the e-book version of the course textbook. For the final exm, the overall average for the entire class was μ = 81.7 but the n = 9 students who used e-books had a mean of M = 72.2 with a standard deviation of s = 5.7 a. is the sample sufficient to condluce that scores for students using e-books were significantly different from scores for the regular class? use a two-tailed test with alpha = .05 b. Construct the 90% confidence interval to estimate the mean exam score if the entire population used e-booksarrow_forward
- The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 ounces with a standard deviation of 0.41. At alpha/a = .05, what is the null hypothesis?arrow_forwardThe Scottsdale fire department aims to respond to fire calls in 8 minutes or less, on average. Response times are normally distributed with a standard deviation of 1 minute 48 seconds. Would a sample of 18 fire calls with a mean response time of 8 minutes 49 seconds provide sufficient evidence to show that the goal is not being met at α = .01? (a) Choose the appropriate hypotheses. H0: µ ≤ 8 min vs H1: µ > 8 min, Reject H0 if zcalc > 2.326 H0: µ ≥ 8 min vs H1: µ < 8 min, Reject H0 if zcalc > 2.326 a b (b) Calculate the value of the test statistic. (Round your answer to 2 decimal places.) zcalc _________ (c) Use Excel to find the p-value. (Round your answer to 4 decimal places.) p-value _________ (d) If α = .01, we would Fail to reject the null hypothesis. Reject the null hypothesis.arrow_forwardIn a random sample of 75 eighth grade students scores on a national mathematics assessment test has a mean score of 266. The test result prompts a state school administration to declare that the mean score for the stated eighth graders on this exam is more than 260. Assume the population standard deviation is 34. At a=0.09, is there enough evidence to support the administrations claim? Write the claim mathematically and identify Ho and Ha Find the standardized test statistic z, and its corresponding areaarrow_forward
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