5, Concern for the continued deterioration of health care in this country has le

Question

5, Concern for the continued deterioration of health care in this country has led to a number of studies. Suppose it is known that in 1980 the average emergency room wait time in Harnett County was 33 minutes. A random sample of 55 people surveyed last year upon exiting the Betsy Johnson Regional Hospital (BJRH) emergency department here in Harnett County showed that they spent an average of 47 minutes per waiting to see a doctor with a standard deviation of 18 minutes. Test at the 5% significance level if the current mean time spent waiting to see a doctor in the BJRH emergency department is greater than 33 minutes. Note that the computed p-value was was 0.0003

Explanation / Answer

Given that,
population mean(u)=33
sample mean, x =47
standard deviation, s =18
number (n)=55
null, Ho: =33
alternate, H1: >33
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.674
since our test is right-tailed
reject Ho, if to > 1.674
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =47-33/(18/sqrt(55))
to =5.7682
| to | =5.7682
critical value
the value of |t | with n-1 = 54 d.f is 1.674
we got |to| =5.7682 & | t | =1.674
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 5.7682 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: =33
alternate, H1: >33
test statistic: 5.7682
critical value: 1.674
decision: reject Ho
p-value: 0.0003

we have evidence that current mean time spent waiting to see a doctor in the BJRH emergency department is great
than 33 minutes.

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