Question

Find a news item (from the internet, a newspaper, a magazine, radio, or television) that reaches a conclusion based on hypothesis test You need discus the following questions:

Describe your case briefly (i.e., a decision process within your work or business interest OR a news item)

Identify the null and alternative hypotheses in your case Identify the population and the sample, to the extent that you can from the information given.

What was the result of their hypothesis test?

Answer 1

PROBLEM-

A study was conducted to determine whether the drug AZT (Zidovudine) was effective in preventing serious opportunistic infection among individuals infected with human immunodeficiency virus (HIV). Individuals who were HIV-positive were randomly selected to either receive AZT treatment or a placebo (Non drug) treatment. Among the 145 individuals who received AZT, 24 developed serious opportunistic infections. Among the 137 individuals who were not treated with AZT, 45 developed serious opportunistic infections. At level of significance 0.01, test whether the drug AZT has satisfactory effect on HIV-positive individuals?

HYPOTHESIS TEST-

We have to perform two sample proportion test. Drug AZT is considered to have significant effect on HIV-positive individuals if proportion of HIV-positive individuals who suffers in opportunistic infection is significantly lesser in case of receiving this drug than that in case of receiving placebo.

Taking HIV-positive individuals who received AZT as first sample and individuals who received placebo as second sample we perform hypothesis test as follows.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

Here,

First sample size

Second sample size

First sample proportion is given by

Second sample proportion is given by

[Using R-code 'pnorm(-3.181329)']

Level of significance

We reject our null hypothesis if

Here, we observe that

So, we reject our null hypothesis.

Hence, based on the given data we can conclude that there is significant evidence that drug AZT has satisfactory effect on HIV-positive individuals.