Doctors nationally believe that 72% of a certain type of operation are successful.In a certain hospital, 53 of these operations were observed, and 63% of them were successful.If , is this hospital's success
Rate different from the national average?
A)No, because the test value -0.86 is in the noncritical region.
B)Yes, because the test value -0.86 is in the critical region.
C)No, because the test value -1.46 is in the noncritical region.
D)Yes, because the test value -1.46 is in the noncritical region.

Question

Doctors nationally believe that 72% of a certain type of operation are successful.In a certain hospital, 53 of these operations were observed, and 63% of them were successful.If  , is this hospital's success
Rate different from the national average?
A)No, because the test value -0.86 is in the noncritical region. 
B)Yes, because the test value -0.86 is in the critical region. 
C)No, because the test value -1.46 is in the noncritical region. 
D)Yes, because the test value -1.46 is in the noncritical region.

Quizplus · Accepted Answer

We need to conduct a hypothesis test to determine if the hospital's success rate is different from the national average. We can use a one-sample proportion test with the following hypotheses:

Null hypothesis: p = 0.72
Alternative hypothesis: p ≠ 0.72

We calculate the test statistic using the formula:

z = (p - P) / sqrt(P*(1-P)/n)

where p is the sample proportion (0.63), P is the population proportion (0.72), and n is the sample size (53).

Plugging in the values, we get:

z = (0.63 - 0.72) / sqrt(0.72*(1-0.72)/53) = -1.46

Using a 95% confidence level with a two-tailed test, the critical values for the test statistic are -1.96 and 1.96. Since our test value of -1.46 falls in the noncritical region (-1.96 < -1.46 < 1.96), we fail to reject the null hypothesis. Therefore, we can conclude that there is not enough evidence to suggest that the hospital's success rate is different from the national average. The correct answer is C.

Doctors Nationally Believe That 72% of a Certain Type of Operation