Question

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 332 people living in East Vancouver and finds that 38 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 0.06. A test of hypothesis is conducted.

Part I:
What is the null hypothesis?

a. The sample proportion of residents who have recently had the flu is lower than 0.06.

b. The sample proportion of residents who have recently had the flu is 0.06.

c. The sample proportion of residents who have recently had the flu is greater than 0.06.

d. The true proportion of residents who have recently had the flu is greater than 0.06.

Part II:
What is the alternative hypothesis?

a. The sample proportion of residents who have recently had the flu is greater than 0.06.

b. The true proportion of residents who have recently had the flu is greater than 0.06.

c. The sample proportion of residents who have recently had the flu is 0.06.

d. The true proportion of residents who have recently had the flu is 0.06.

Part III:
Assuming that 6% 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. N(0.06, 4.32722)

b. N(0.06, 0.00072)

c. N(0.06, 0.23749)

d. Bin(332, 0.06000)

e. N(0.06, 0.01303)

Part IV:
Assuming that 6% of all East Vancouver residents have recently had the flu, is the observed proportion based on the 332 sampled residents unusually low, high, or neither?

a. Neither

b. Unusually high

c. Unusually low

Answer 1

The null hypothesis is that the sample proportion is lower than 0.06, while the alternative hypothesis is that it is greater than 0.06. Assuming a population flu rate of 6%, the sample proportion of residents who have recently had the flu follows a binomial distribution. The observed proportion in the sample is unusually low.

Step-by-step explanation:

Part I: The null hypothesis in this case is option a: The sample proportion of residents who have recently had the flu is lower than 0.06.

Part II: The alternative hypothesis is option a: The sample proportion of residents who have recently had the flu is greater than 0.06.

Part III: Assuming that 6% of all East Vancouver residents have recently had the flu, the sample proportion of residents who have recently had the flu follows a binomial distribution, which is represented by option d: Bin(332, 0.06000).

Part IV: Assuming that 6% of all East Vancouver residents have recently had the flu, the observed proportion based on the 332 sampled residents is unusually low.