Question

2. A random sample of 100 patients with virus found that it was fatal in 18 people and 182 people eventually made a full recovery. In a random sample of 300 SARS patients, 34 died.

a.) Verify your conditions for inference

b.) Calculate a 90% confidence interval for the true mean difference in the proportion of virus cases that were fatal and the proportion of SARS cases that were fatal.

c.) If you were to create a 95% confidence interval, would it be wider or narrower?

Answer 1

2.

a)

The following conditions should be met for inference:

Normality

We assume that normality is met. More specifically, we require that :

• 
• 
• 
• 

Hence all conditions are met.

SRS Condition

The sampling method for each population is simple random sampling as mentioned above.

Independence

The samples are independent of each other.

b)

The critical value for α=0.1 is .

The corresponding confidence interval is computed as shown below:

Therefore, based on the data provided, the 90% confidence interval for the difference between the population proportions p1​−p2​ is −0.003<p<0.137, which indicates that we are 90% confident that the true difference between population proportions is contained by the interval (−0.003,0.137).

c)

Increasing the confidence interval would widen the interval. The higher the confidence interval, the higher(wider) is the range of the values.

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