In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

8 out of the 20 teams in the sample had a season winning percentage better than 0.500. This means that $n = 20, \pi = \frac{8}{20} = 0.4$ .

95% confidence interval

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 1.96\sqrt{\frac{0.6*0.4}{20}} = 0.1853$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 1.96\sqrt{\frac{0.6*0.4}{20}} = 0.6147$

The 95% confidence interval for the true proportion of all teams that had a season winning percentage better than 0.500 is (0.1853, 0.6147).

3 0

4 years ago

Can someone help me out ???

Vsevolod [243]

Answer: 3/8

Step-by-step explanation:

4 0

3 years ago

5x(2)<br> Explain to me please<br> Thanks

yuradex [85]

Answer:

10x

Step-by-step explanation:

5x(2)

When this is simplified, the answer is 10x

5x(2)

5x multiplied by 2 is 10x

5 0

4 years ago

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Which prism has a volume of 5 cubic units? 1 and one-half units by 3 units by 1 unit A rectangular prism. 2 units by 2 units by

andriy [413]

Step-by-step explanation:

You can multiply each of these values together to get the volume of the rectangular prism. The volume of the rectangular prism is 10 cubic units or units3. The units are cubic units because you multiplied the units 3 times when you multiplied the height, length, and width.

8 0

3 years ago

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