Question

Suppose a new cancer treatment was given to a sample of 300 patients. The treatment was successful for 210 of the patients. Assume that these patients are representative of the population for whom the treatment would be successful, including a margin error.

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Answer 1

a. 70% ± 5.3%

Explanation:

Supposing a new cancer treatment was given to a sample of 300 patients and the treatment was successful for 210 of the patients. These patients are representative of the population for whom the treatment would be successful, including a margin error. Therefore, the answer is 70% ± 5.3%.

Answer 2

a. 70% ± 5.3%

Explanation:

The proportion is:

p = 210 / 300 = 0.7

The margin of error is:

ME = z √(p (1 − p) / n)

where z is the critical value, p is the proportion, and n is the sample size.

For a 95% confidence interval, z ≈ 2.

ME = 2 √(0.7 (1 − 0.7) / 300)

ME = 0.053

So the proportion is 70% ± 5.3%.