Answer:
Step-by-step explanation:
This is a test of 2 population proportions. Let 1 and 2 be the subscript for the men and women who own cats respectively. The population proportion of men and women who own cats would be p1 and p2 respectively.
p1 - p2 = difference in the proportion of men and women who own cats.
The null hypothesis is
H0 : p1 = p2
p1 - p2 = 0
The alternative hypothesis is
Ha : p1 ≠ p2
p1 - p2 ≠ 0
it is a two tailed test
Sample proportion = x/n
Where
x represents number of success
n represents number of samples
For men
n1 = 80
p1 = 55/100 = 0.55
x1 = p1n1 = 0.55 × 80 = 44
For women,
n2 = 100
p2 = 30/100 = 0.3
x2 = p2n2 = 0.3 × 100 = 30
The pooled proportion, pc is
pc = (x1 + x2)/(n1 + n2)
pc = (44 + 30)/(80 + 100) = 0.41
1 - pc = 1 - 0.41 = 0.59
z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)
z = (0.55 - 0.3)/√(0.41)(0.59)(1/80 + 1/100) = 3.39
Test statistic = 3.39
We have been given that a retailer buys cases of 24 shirts for $30/case and then resells them in packs of 5 for $8/pack.
Further, we know that retailer sold all the shirts he purchased and profited $84 on the sale.
Let us first find LCM of 24 and 5. The LCM is 120.
Now, let us assume that the retailer bought 120x shirts. Therefore total profit will be:
We can set this equal to the given profit to figure out the value of x first.
Therefore, the retailer sold 120(2)=240 shirts, that is, 48 packs.
Hello there!
(5x - 2)(4x² - 3x - 2)
Use the distributive property
=(5x)(4x²) + (5x)(-3x) + (5x)(-2) + (-2)(4x²) + (-2)(-3x)² + (-2)(-2)
= 20x³ - 15x² - 10x - 8x² + 6x + 4
= 20x³ - 23x² -4x + 4
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