A recent survey showed that from a sample of 500 packages delivered by a Postal Service, 480 were delivered on time. a) Construct a 95% confidence interval for the proportion of all packages that are delivered on time by the Postal Service. b) The manager of the Postal Services claims that 98 percent of their mail are delivered on time. He wants to test at the 1% significance level to determine whether the true proportion is less than 98 percent. i. Give the null and alternative hypothesis of this test. ii. Determine the critical value(s) of this test. iii. Compute the value of the test statistic. iv. State the decision rule. v. Give your decision based on the available sample evidence. vi. Hence, state your conclusion.

A recent survey showed that from a sample of 500 packages delivered by a Postal Service, 480 were delivered on time. a) Construct a 95% confidence interval for the proportion of all packages that are delivered on time by the Postal Service. b) The manager of the Postal Services claims that 98 percent of their mail are delivered on time. He wants to test at the 1% significance level to determine whether the true proportion is less than 98 percent. i. Give the null and alternative hypothesis of this test. ii. Determine the critical value(s) of this test. iii. Compute the value of the test statistic. iv. State the decision rule. v. Give your decision based on the available sample evidence. vi. Hence, state your conclusion.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

See similar textbooks

Similar questions

What is meant by the sample space of an experiment?
A new television series must prove that it has more than 25% of the viewing audience after its initial 13-week run in order to be judged successful. Assume that in a sample of 400 households, 112 were watching the series. (b) Find a 99% confidence interval for the proportion of the viewing audience after its initial 13-week run
Construct a 99% confidence interval for the proportion of all motorbike license applications that are misplaced by the department of transport, if a survey found that 20 out of a sample of 175 applications had been misplaced.
The St. Lucie County Economic Development Board needs to estimate the proportion of all county residents who have earned at least a bachelor's degree. A random sample conducted by the St. Lucie County Economic Development Board found that 19.3% of all county residents held at least a bachelor's degree.Find three different confidence intervals - one with sample size 254, one with sample size 478, and one with sample size 668. Assume that 19.3% of the county residents in each sample have earned at least a bachelor's degree. Notice how the sample size affects the margin of error and the width of the interval.Report confidence interval solutions using interval notation. Report all solutions in percent form, rounded to two decimal places, if necessary. When n=254, the margin of error for a 97% confidence interval is given by .When n=254, a 97% confidence interval is given by . When n=478, the margin of error for a 97% confidence interval is given by .When n=478, a 97% confidence interval…
calculate a 95% confidence interval for the proportion of U.S residents who feel that the united states is on the right track in terms of its foreign policy if a random sample of 400 such residents had 148 respond yes
The Okeechobee County Economic Development Board needs to estimate the proportion of all county residents who have earned at least a bachelor's degree. A random sample conducted by the Okeechobee County Economic Development Board found that 10.5% of all county residents held at least a bachelor's degree.Find three different confidence intervals - one with sample size 180, one with sample size 451, and one with sample size 621. Assume that 10.5% of the county residents in each sample have earned at least a bachelor's degree. Notice how the sample size affects the margin of error and the width of the interval.Report confidence interval solutions using interval notation. Report all solutions in percent form, rounded to two decimal places, if necessary. When n=180n=180, the margin of error for a 95% confidence interval is given by .When n=180n=180, a 95% confidence interval is given by . When n=451n=451, the margin of error for a 95% confidence interval is given by .When n=451n=451, a…
The St. Lucie County Economic Development Board needs to estimate the proportion of all county residents who have earned at least a bachelor's degree. A random sample conducted by the St. Lucie County Economic Development Board found that 20.8% of all county residents held at least a bachelor's degree.Find three different confidence intervals - one with sample size 487, one with sample size 777, and one with sample size 938. Assume that 20.8% of the county residents in each sample have earned at least a bachelor's degree. Notice how the sample size affects the margin of error and the width of the interval.Report confidence interval solutions using interval notation. Report all solutions in percent form, rounded to two decimal places, if necessary. When n=487n=487, the margin of error for a 95% confidence interval is given by .When n=487n=487, a 95% confidence interval is given by . When n=777n=777, the margin of error for a 95% confidence interval is given by .When n=777n=777, a 95%…
In an October 2003 poll conducted by the Gallup organization, 684 of 1006 randomly selected adults aged 18 or older stated they think the government should make partial birth abortions illegal, except in cases necessary to save the mother. construct a 95 percent confidence interval for the proportion of adults 18 and older who think the government should make partial birth abortions illegal, except in cases necessary to save the mother and interpret the interval.
In order to estimate the overall proportion of students who favor a shorter semester system, we selected a simple random sample of 36 students and found that 24 of them favor a shorter semester system.(a) Construct a 90% confidence interval for the overall proportion of students who favor a shorter semester system.(b) Find the margin of error associated with this c.i. and interpret the answer in plain language.(c) In order for the margin of error to be no greater than 0.1 (or 10 percentage points), how large a sample should be drawn instead?
In a random sample of 50 patients undergoing a standard surgical procedure, 15 required medication for post operative pain. In a random sample of 90 patients undergoing a new procedure, only 16 required pain medication. a)Are conditions met to perform inference onthis study? b)Construct and interpret a 95% confidence interval for the difference in the proportions of patients needing pain medication between the old and new procedures. c) A physician claims that the proportion of patients who need pain medication is the same for both procedures. Does the confidence interval contradict this claim? Why/Why not?
Construct a 99% confidence interval for the true proportion of all car license applications that are misplaced by the licensing department, if a survey found that 25 out of a sample of 155 applications had been misplaced.
In September 2011, Gallup surveyed 1,004 American adults and asked them whether they blamed Barack Obama a great deal, a moderate amount, not much, or not at all for U.S. economic problems. The results showed that 53% of respondents blamed Barack Obama a great deal or a moderate amount. Calculate the 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems.