Question

Turan et al (2015) cite previous research on the prevalence of SSIs in colorectal surgery suggesting that the rate is about 11% or higher. The contraction rate of SSIs in the seasonal effect data for the spring, summer, and autumn months is 7.49%, well below the previous 11% threshold. The researchers use this information to make a guess that in the winter months alone, the rate will also be below 11%, but probably higher than the 7.49%. The researchers find that 92 out of 930 patients undergoing surgery in the winter months contracted an SSI. Use this information to answer questions 1-4.

Conduct the following hypothesis test:

• A one-tail Z-test for a one-sample proportion at the 95% confidence level
• with Null Hypothesis that the proportion of patients that will contract an SSI is equal to 0.11
• and with Alternate Hypothesis that the proportion of patients that will contract an SSI is less than 0.11

1. Identify the correct critical value, Z_α. (10%)
2. Calculate the test statistic, Z_test. (10%)
3. Calculate the p-value, P(Z < Z_test). (10%)
4. Compare the test statistic to the critical value. Compare the p-value to the significance level α. Compare the sample proportion to the null hypothesis proportion by calculating the rate difference and the rate ratio. Is there a statistically significant difference to suggest that the SSI rate in winter is less than 11%? Is there a practically significant difference? (15%)

Answer 1

given

sample size =n=930

x=92

we have to test

H0: P=0.11

H1: P<0.11

a)

at alpha =0.1 the critical value is given by

so

b)

c)

P Value =P(Z<-1.078) =0.140

d)

since its left tailed test so since Test statistics >Critical value hence we failed to reject the null hypothesis

also P Value > level of significance hence we failed to reject the null hypothesis

Hence we fail to reject the Hypothesis P=0.11