Hospital emergency rooms (ERs) have a bad reputation forlong wait times. To improve their image, many hospitalshave worked hard to reduce their ER wait times andfrequently advertise their improved, low ER wait times.Lawnwood Regional Medical Center recently advertised a 4minute or less wait time at their ER. An accreditationagency is suspicious of this low advertised wait time andwould like to test the hospital's claim.A random sample of 139 ER visits to Lawnwood RegionalMedical Center was examined and the mean wait time ofthe sample was found to be 4.18 minutes.Using a significance level of 2.5%, can the accreditationagency conclude that the hospital's claim about ER waittimes is false? Assume that the standard deviation of thewait times of all ER visits at Lawnwood Regional MedicalCenter is known to be 0.71 minutes. Use the critical valuemethod.State the null and alternative hypothesis for this test.Ho: ?H₁: ?Determine if this test is left-tailed, right-tailed, or two-tailed.two-tailedleft-tailedOright-tailedShould the standard normal (z) distribution or Student's (t)distribution be used for this test?The Student's t distribution should be usedThe standard normal (z) distribution should be usedDetermine the critical value(s) for this hypothesis test.Round the solution (s) to two decimal places. If more thanone critical value exists, enter the solutions using acomma-separated list Should the standard normal (z) distribution or Student's (t)distribution be used for this test?The Student's t distribution should be usedThe standard normal (z) distribution should be usedDetermine the critical value(s) for this hypothesis test.Round the solution (s) to two decimal places. If more thanone critical value exists, enter the solutions using acomma-separated list.Determine the test statistic. Round the solution to twodecimal places.Determine the appropriate conclusion for this hypothesistest.The sample data provide sufficient evidence toreject the alternative hypothesis that the mean ERwait time at is greater than 4 minutes and thus weconclude that the hospital's claim that the mean ERwait time is 4 minutes or less is likely true.The sample data provide sufficient evidence toreject the null hypothesis that the mean ER waittime at is 4 less minutes and thus we conclude thatthe hospital's claim that the mean ER wait time is 4or less minutes is likelyThe sample data do not provide sufficient evidenceto reject the null hypothesis that the mean ER waittime at is 4 less minutes and thus we conclude thatthe hospital's claim that the mean ER wait time is 4or less minutes is likely true.The sample data do not provide sufficient evidenceto reject the alternative hypothesis that the meanER wait time at is greater than 4 minutes and thuswe conclude that the hospital's claim that the meanER wait time is 4 minutes or less is likely false.

Question

Accepted Answer

Given,
sample size (n) = 139
sample mean (x̄) = 4.18
population mean ( µ ) = 4
 sample standard…

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