# HOMEWORK

**Question 1**

A national survey was initiated and intended to capture the prevalence of HIV in the post-HAART (Highly active anti-retroviral therapy) era of treatment. Out of a sample of 1,483 participants, a total of 241 were found to be HIV positive.

A) Calculate a SE.

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**Question 2**

Suppose a national survey intends to identify the prevalence of Hepatitis C in a population of intravenous drug users. Out of a sample of 6,458 a total of 754 were confirmed to have the disease.

A) Calcuate a SE using the plus-four method.

B) Construct a 99% confidence interval about the estimate.

**Question 3**

A national organization sets out to investigate the change in prevalence of HIV since the last census in 2010. A total of 4,706 participants were interviewed and a total of 468 responses were confirmed to be HIV positive. Assume that the data from the census indicated that the prevalence of HIV in the particular population was 7.5%.

A) Write out the null and alternative hypotheses for a formal test of significance.

B) Interpret your results at 95% confidence.

**Question 4**

The national blood bank sponsored by the US estimates that approximately 38% of the population has blood type O+. Suppose a local blood bank samples 14 participants, and determines that 8 participants are O+.

A) Can we approximate by the normal distribution in this instance?

B) Depending on your decision in part A), carry out a test to determine if the proportion of responses based on the local blood bank differ significantly from those at the national blood bank.

**Question 5**

A researcher is interested in conducting an observational study looking at the incidence of breast cancer in women 40-65 years of age followed for a period of 15 years. The researcher is interested in showing that the incidence of breast cancer has risen from 24% to 35% since the last surveillance data was published covering this population. If the researcher wants to be 95% confident with 90% power, how many participants should be enrolled?