Question

In 2016, the US Department of Agriculture established a “maximum acceptable” salmonella
prevalence of 15.4 percent for chicken parts sampled at the end of a slaughterhouse’s kill line. 54 of the
154 largest chicken-slaughter facilities in the US failed to meet this standard in 2018. Assume that these
results are representative for all large chicken-slaughter facilities. Suppose that in a random sample of 60
chicken parts from the large ACME chicken-slaughter facility (which produces 1,000,000 chicken parts
per year), 45 chicken parts test negative for salmonella.

b) Report a point estimate for the prevalence of salmonella among ACME chicken parts, and test whether
this prevalence is equal to the maximum acceptable value.

Answer 1

Number of chickens found positive in ACME chicken-slaughter facility is

The point estimate for the prevalence of salmonella among ACME chicken parts is

IN order to test whether
this prevalence is equal to the maximum acceptable value. Define the null and the alternative hypothesis as

The value of the test static is

Now, since the test is two tailed test, we set the significance level

Now, the P-value is Using Normal table

As 0.0394<0.05

We reject the null hypothesis,

Hence there is enough evidence to conclude that the prevalence is not equal to the maximum acceptable val