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Vsevolod [243]
3 years ago
12

Sooooooooo technically i've neevr lost a fight with a tiger

Mathematics
1 answer:
Aloiza [94]3 years ago
3 0

Answer:

oh thats cool

Step-by-step explanation:

 

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Answer:

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Step-by-step explanation:

Using the identity

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\frac{1-tan^2x}{1+tan^2x}

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In a survey of 1000 randomly selected adults in the United States, participants were asked what their most favorite and what the
xenn [34]

Answer:

(a) The 95% confidence interval for the population proportion of US adults for whom math was their most favorite subject is (0.204, 0.256).

(b) The 95% confidence interval for the population proportion of US adults for whom math was their least favorite subject is (0.34, 0.40).

Step-by-step explanation:

The questions are:

(a) Construct and interpret a 95% confidence interval for the proportion of US adults for whom math was their most favorite subject.

(b) Construct and interpret a 95% confidence interval for the proportion of US adults for whom math was their least favorite subject. Solution:

(a)

The 95% confidence interval for the population proportion is:

CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

Th information provided is:

<em>n</em> = 1000

Number of US adults for whom math was their most favorite subject

= <em>X</em>

= 230

Compute the sample proportion of US adults for whom math was their most favorite subject as follows:

\hat p=\frac{230}{1000}=0.23

The critical value of <em>z</em> for 95% confidence interval is:

z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

Compute the 95% confidence interval for the population proportion of US adults for whom math was their most favorite subject as follows:

CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

     =0.23\pm 1.96\sqrt{\frac{0.23(1-0.23)}{1000}}\\=0.23\pm 0.0261\\=(0.2039, 0.2561)\\\approx (0.204, 0.256)

Thus, the 95% confidence interval for the population proportion of US adults for whom math was their most favorite subject is (0.204, 0.256).

(b)

The 95% confidence interval for the population proportion is:

CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

Th information provided is:

<em>n</em> = 1000

Number of US adults for whom math was their least favorite subject

= <em>X</em>

= 370

Compute the sample proportion of US adults for whom math was their least favorite subject as follows:

\hat p=\frac{370}{1000}=0.37

The critical value of <em>z</em> for 95% confidence interval is:

z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

Compute the 95% confidence interval for the population proportion of US adults for whom math was their least favorite subject as follows:

CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

     =0.37\pm 1.96\sqrt{\frac{0.37(1-0.37)}{1000}}\\=0.37\pm 0.0299\\=(0.3401, 0.3999)\\\approx (0.34, 0.40)

Thus, the 95% confidence interval for the population proportion of US adults for whom math was their least favorite subject is (0.34, 0.40).

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