The waiting time for patients at local walk-in health clinic follows a normal di
ID: 3223839 • Letter: T
Question
The waiting time for patients at local walk-in health clinic follows a normal distribution with a population mean of 15 minutes and a population standard deviation of 5 minutes. The quality-assurance department found in a sample of 50 patients that the mean waiting time was 13.25 minutes. At the 0.01 significance level, decide if the sample data support the claim that the mean waiting time is less than 15 minutes. Complete steps 1 through 6 below. State the null hypothesis and the alternate hypothesis. State the level of significance. State the test statistic. Formulate the decision rule. Make a decision. Please show your work. Please show your work as you determine the p-value. Interpret the result of the hypothesis test.Explanation / Answer
6) 1 ) null hypothesis: Ho: mean =15
alternate hypothesis: Ha: mean<15
level of significance =0.05
for std error =std deviation/(n)1/2 =0.707
hence test stat z=(X-mean)/std error =(13.25-15)/0.7071 =-2.4749
decision rule: critical value =-1.645 ; reject Ho : if test stat <-1.645
as our test stat z is less then critical value we reject null hypothesis.
6) as it is left hand test ; fromo normal value table for z=-2.4749 ; p value =0.0067 ( ti-84 ---normalcdf(-2.4749,-10)
as p value is less then 0.05 level ; we reject null hypothesis
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