A study was conducted to investigate whether a new drug could significantly reduce pan in people with arthritis. From a group of 500 people with arthritis 250 were randomly assigned to receive the drug (group 1) and the remaining people were assigned a placebo (group 2). After one month of treatment, 225 people in group 1 reported pain relief and 150 people in group 2 reported pain relief Let Pe represent the combined (or pooled) sample proportion for the two samples. Have the conditions for inference for testing the difference in population proportions been met?

a. No. The people in the study were not selected at random.
b. No. The number of people in the study was too large compared with the size of the population.
c. No. The normality of the sampling distribution cannot be assumed because Pe times each sample size is not sufficiently large.
d. No. The normality of the sampling distribution cannot be assumed because (1 - Pe) times each sample size is not sufficiently large.
d. Yes. All conditions for inference have been met.

From a group of 500 people with arthritis 250 were randomly assigned to receive the drug (group 1) and the remaining people were assigned a placebo (group 2).

It is given that the people in the study were selected randomly.

The pooled proportion is given by

Pe = no. of people who reported pain relief in both groups/total number of people

Pe = (225 + 150)/500

Pe = 375/500

Pe = 0.75

Now let us check the condition np ≥ 10

250*0.75

187.5 ≥ 10

Satisfied

Now let us check the condition n(1 - p) ≥ 10

250(1 - 0.75)

250*0.25

62.5 > 10

Satisfied

Therefore, all conditions for inference have been met option d is the correct option.

Omm2 Omm2 · Answer 2 · 2022-03-14T07:34:04+01:00

A correct option is an option (e).

Pooled proportion:

we have sample information from the populations that have the same proportion.

That is when we would use the concept of pooled proportions,

It is given that in group 1 the number of people is 225 and in group 2 the number of people is 150

Then the pooled proportion is,

[tex]\frac{225+150}{500}=0.75\\ 0.75\times 250=18.75 \ge10\\(1-0.75)250=62.5\ge10[/tex]

Hence, yes, all conditions for inference have been met.

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