The total number of yards is 360 yards
<h3>How to determine the number of yards?</h3>
The given parameters are:
Number of sheets = 8
Yard per sheet = 45 yards
The total number of yards is calculated as:
Total number of yards = Number of sheets * Yard per sheet
Substitute the known values in the above equation
Total number of yards = 8 * 45 yards
Evaluate the product
Total number of yards = 360 yards
Hence, the total number of yards is 360 yards
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Answer:
There is a significant difference between the two proportions.
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for difference between population proportions is:
![CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}](https://tex.z-dn.net/?f=CI%3D%28%5Chat%20p_%7B1%7D-%5Chat%20p_%7B2%7D%29%5Cpm%20z_%7B%5Calpha%2F2%7D%5Ctimes%5Csqrt%7B%5Cfrac%7B%5Chat%20p_%7B1%7D%281-%5Chat%20p_%7B1%7D%29%7D%7Bn_%7B1%7D%7D%2B%5Cfrac%7B%5Chat%20p_%7B2%7D%281-%5Chat%20p_%7B2%7D%29%7D%7Bn_%7B2%7D%7D%7D)
Compute the sample proportions as follows:
![\hat p_{1}=\frac{80}{250}=0.32\\\\\hat p_{2}=\frac{40}{175}=0.23](https://tex.z-dn.net/?f=%5Chat%20p_%7B1%7D%3D%5Cfrac%7B80%7D%7B250%7D%3D0.32%5C%5C%5C%5C%5Chat%20p_%7B2%7D%3D%5Cfrac%7B40%7D%7B175%7D%3D0.23)
The critical value of <em>z</em> for 90% confidence interval is:
![z_{0.10/2}=z_{0.05}=1.645](https://tex.z-dn.net/?f=z_%7B0.10%2F2%7D%3Dz_%7B0.05%7D%3D1.645)
Compute a 90% confidence interval for the difference between the proportions of women in these two fields of engineering as follows:
![CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}](https://tex.z-dn.net/?f=CI%3D%28%5Chat%20p_%7B1%7D-%5Chat%20p_%7B2%7D%29%5Cpm%20z_%7B%5Calpha%2F2%7D%5Ctimes%5Csqrt%7B%5Cfrac%7B%5Chat%20p_%7B1%7D%281-%5Chat%20p_%7B1%7D%29%7D%7Bn_%7B1%7D%7D%2B%5Cfrac%7B%5Chat%20p_%7B2%7D%281-%5Chat%20p_%7B2%7D%29%7D%7Bn_%7B2%7D%7D%7D)
![=(0.32-0.23)\pm 1.645\times\sqrt{\frac{0.32(1-0.32)}{250}+\frac{0.23(1-0.23)}{175}}\\\\=0.09\pm 0.0714\\\\=(0.0186, 0.1614)\\\\\approx (0.02, 0.16)](https://tex.z-dn.net/?f=%3D%280.32-0.23%29%5Cpm%201.645%5Ctimes%5Csqrt%7B%5Cfrac%7B0.32%281-0.32%29%7D%7B250%7D%2B%5Cfrac%7B0.23%281-0.23%29%7D%7B175%7D%7D%5C%5C%5C%5C%3D0.09%5Cpm%200.0714%5C%5C%5C%5C%3D%280.0186%2C%200.1614%29%5C%5C%5C%5C%5Capprox%20%280.02%2C%200.16%29)
There will be no difference between the two proportions if the 90% confidence interval consists of 0.
But the 90% confidence interval does not consists of 0.
Thus, there is a significant difference between the two proportions.
Answer:
19 squared units
Step-by-step explanation:
To find the area of the figure, you can simply count the number of squares that are shaded. I counted a total of 19 squares, meaning that the total area of the shaded figure is 19 units squared.