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3 years ago

Question

Mathematics

1 answer:

Rus_ich [418]3 years ago

8 0

9514 1404 393

Answer:

S = 4.5π ≈ 14.14 units

Step-by-step explanation:

The arc length is given by ...

s = rθ . . . . . r = radius; θ = central angle in radians

The angle 135° is ...

135° = 135°(π/180°) = 3π/4 radians

The arc of interest has length ...

s = 6×3π/4 = 9/2π ≈ 14.14 . . . units

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According to the U.S. Census Bureau, 42% of men who worked at home were college graduates. In a sample of 480 women who worked a

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Answer:

1) $0.327 - 0.539 \sqrt{\frac{0.327(1-0.327)}{480}}=0.315$

The point estimate for the proportion of college graduates among women who work at home is 0.327

2) $0.327 - 0.539 \sqrt{\frac{0.327(1-0.327)}{480}}=0.315$

$0.327 + 0.539 \sqrt{\frac{0.327(1-0.327)}{480}}=0.339$

The 80% confidence interval is given by (0.315; 0.339)

Step-by-step explanation:

For this case we have the following info given:

$X = 157$ represent the women who worked at home who were college graduates

$n = 480$ the sample size selected

Part 1

In order to find the proportion of college graduates among women who work at home and we can use the following formula:

$\hat p=\frac{X}{n} = \frac{157}{480}= 0.327$

The point estimate for the proportion of college graduates among women who work at home is 0.327

Part 2

Construct an 80% confidence interval for the proportion of women who work at home who are college graduates. Round the answer to three decimal places. An 80% confidence interval for the proportion of women who work at home Is < p <

The confidence interval for the true proportion would be given by this formula

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

For the 80% confidence interval the value for the significance is $\alpha=1-0.8=0.2$ and $\alpha/2=0.1$ , the critical value would be given by:

$z_{\alpha/2}=0.539$

And replacing we goot:

$0.327 - 0.539 \sqrt{\frac{0.327(1-0.327)}{480}}=0.315$

$0.327 + 0.539 \sqrt{\frac{0.327(1-0.327)}{480}}=0.339$

The 80% confidence interval is given by (0.315; 0.339)

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