Question
show all work please
For each of the following problems, please provide the requested information. State the null and alternate hypotheses and the level of significance. Is the test left-tailed, right-tailed, or two-tailed? Identify the appropriate sampling distribution: the standard normal or the Student's t. What is the value of the sample test statistic? Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P- value. Find the critical value(s). Based on your answers for parts (a) through (d), will you reject or fail to reject the null hypothesis? Interpret your conclusion in the context of the application. Long term experience showed that after a type of eye surgery, recovery time had a mean of mu = 5.3 days in a hospital. However, a random sample of 32 patients with this type of eye surgery were recently treated as outpatients during the recovery. The sample mean recovery time was x = 4.2 days. Does this indicate that the mean recovery time for outpatients is less than the time for those recovering in the hospital? Use a 1% level of significance and assume sigma = 1.9 days.
Explanation / Answer
1)THE NULL HYPOTHES = Ho= u = 5.3
THE ALTERNATE HYPOTHESIS = Ha = u<5.3
the level of significance = 0.01
as n = 32>30 hence it will be normal z test
the critical region = z<-2.33
the z stat = (4.2 - 5.3)/(1.9/sqrt(32))
z stat = -3.28
p value = 0.0005
as the p value is less then the significance level we will not reject the null hypothesis
