An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 336 people living in East Vancouver and finds that 36 have recently had the flu.

The epidemiologist will recommend East Vancouver as a location for one of the vaccination programs if her sample data provide sufficient evidence to support that the true proportion of people who have recently had the flu is greater than 0.05. A test of hypothesis is conducted.

Part i) What is the null hypothesis?

A. The true proportion of residents who have recently had the flu is lower than 0.05.
B. The true proportion of residents who have recently had the flu is 0.05.
C. The true proportion of residents who have recently had the flu is greater than 0.05.
D. The sample proportion of residents who have recently had the flu is 0.05.
E. The sample proportion of residents who have recently had the flu is greater than 0.05.
F. The sample proportion of residents who who have recently had the flu is lower than 0.05.

Part ii) What is the alternative hypothesis?

A. The true proportion of residents who have recently had the flu is greater than 0.05.
B. The sample proportion of residents who have recently had the flu is greater than 0.05.
C. The true proportion of residents who have recently had the flu is 0.05.
D. The sample proportion of residents who have recently had the flu is 0.05.
E. The true proportion of residents who have recently had the flu is lower than 0.05.
F. The sample proportion of residents who have recently had the flu is lower than 0.05.

Part iii) Assuming that 5% of all East Vancouver residents have recently had the flu, what model does the sample proportion of residents have recently had the flu follow?

A. Bin( 336, 0.05000 )
B. N( 0.05, 3.99500 )
C. N( 0.05, 0.21794 )
D. N( 0.05, 0.00065 )
E. N( 0.05, 0.01189 )

Part iv) Assuming that 5% of all East Vancouver residents have recently had the flu, is the observed proportion based on the 336 sampled residents unusually low, high or neither?

A. neither
B. unusually low
C. unusually high