Question

- (22.03) About 90% of young adult Internet users (aged 18 to 29) use social network sites. Suppose that a sample survey contacts an SRS of 1500 young adult Internet users and calculates the proportion p in

this sample who use social network sites.
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Step 1:
What is the standard deviation of P (Round your answer to 4 decimal places.)

Answer 1

- Sample Proportion of 1500 young adult Internet users = 0.90

- Sample Mean of 1500 young adult Internet users = 1350

- Standard deviation of the sample proportion = 0.0077 to 4 d.p.

Explanation:

The Central limit theorem explains that for a random sample obtained from an independent distribution, the sampling distribution is approximately normal, with a sample proportion that is approximately equal to the population proportion and the standard deviation of sample proportion is given as

σₓ = √[p(1-p)/n]

So, sample proportion = population proportion

p = p₀ = 90% = 0.90

Sample mean = np

where n = sample size = 1500

p = sample proportion = 0.90

Sample Mean of 1500 young adult Internet users = 1500 × 0.90 = 1350

Standard deviation of sample proportion

= σₓ = √[p(1-p)/n]

= √(0.90×0.10/1500) = 0.0077459667

= 0.0077 to 4 d.p.

Hope this Helps!!!