Question

Please use Rstudio to answer the following question. Thank you.

In a double-blind experiment, healthy volunteers agreed to be exposed to a cold virus. They were either assigned to a control group (no echinacea but a placebo) or the group with echinacea. Here are the results Placebo group: 103 subjects 88 got a cold Echinacea group: 48 subjects 44 got a cold.

a. Calculate the proportions getting cold in each group.

b. Use a two-sample test to compare the proportions. In this case, use a continuity correction.

c. Give a 95% confidence interval for the difference comparing echinacea and placebo.

d. Comment on possible odditites in the study design?  

Answer 1

a)

Given,

Placebo group:

Sample proportion,

Echinacea group:

Sample proportion,

-------------------------------------------------------------------------------------------------------------

b)

Our hypothesis is,

Test statistics:

Where,

Using continuity correction subtract 0.5 from the absolute value i.e. 1.075-0.5 = 0.575

At 0.05 level of significance, critical z value is 1.96

Since, calculated z value is less than the critical z value, i.e.,

Therefore, we conclude that the proportion of two groups are insignificant.

-------------------------------------------------------------------------------------------------------------------------------

c).

95% confidence interval for