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A growth-mindset researcher plans to take an SRS of 200 teenagers from the population of teenagers in North America to see what proportion of teenagers sampled are pursuing a goal they have set for themselves. Suppose that 75% of teenagers in North America are pursuing a goal they have set for themselves. Let p represent the proportion of a sample of 200 teenagers in North America who are pursuing a goal they have set for themselves. What are the mean and standard deviation of the sampling distribution of p?

Sagot :

Answer:

The mean of the sampling distribution of p is 0.75 and the standard deviation is 0.0306.

Step-by-step explanation:

Central Limit Theorem:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

75% of teenagers in North America are pursuing a goal they have set for themselves.

This means that [tex]p = 0.75[/tex]

Sample of 200.

This means that [tex]n = 200[/tex].

What are the mean and standard deviation of the sampling distribution of p?

By the Central Limit Theorem

Mean [tex]\mu = p = 0.75[/tex]

Standard deviation [tex]s = \sqrt{\frac{0.75*0.25}{200}} = 0.0306[/tex]

The mean of the sampling distribution of p is 0.75 and the standard deviation is 0.0306.

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