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hammer [34]
2 years ago
7

In a representative sample of 1000 adult Americans, only 400 could name at least one justice who is currently serving on the U.S

. Supreme Court. Using a significance level of 0.01, carry out a hypothesis test to determine if there is convincing evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court. (For z give the answer to two decimal places. For P give the answer to three decimal places.)
z=
p=
Mathematics
1 answer:
lys-0071 [83]2 years ago
8 0

Answer:

1) z = -6.32

2) p-value = 0.001 × 10^(-2)

3) we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court

Step-by-step explanation:

We are told that In a representative sample of 1000 adult Americans, only 400 could name at least one justice.

Thus:

Sample proportion; p^ = 400/1000 = 0.4

Sample size: n = 1000

We want to find if there is convincing evidence to support the claim that fewer than half of adult Americans can name at least one justice.

Thus, the hypothesis is defined as;

Null hypothesis:H0: p ≥ 0.5

Alternative hypothesis: Ha < 0.5

Formula for the test statistic is;

z = (p^ - p)/√(p(1 - p)/n)

Plugging in the relevant values;

z = (0.4 - 0.5)/√(0.5(1 - 0.5)/1000)

z = -6.32

From online p-value from z-score calculator attached, using z = -6.32; significance level of 0.01; one tailed hypothesis;

We have:

p-value = 0.00001 = 0.001 × 10^(-2)

The p-value is less than the significance level and so we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court

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Step-by-step explanation:

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Find the slope of a line parallel to a line that contains the points (8, -3) and (2, 5).
Illusion [34]

Answer:

-\frac{4}{3}(Your answer choices were really confusing, so I just put the plain answer)

Step-by-step explanation:

To find the slope of a line with just two points, we can use the formula \frac{y2-y1}{x2-x1}. In this case, \frac{5-(-3)}{2-8}. This is \frac{8}{-6}. This reduces to -\frac{4}{3}

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2 years ago
A company sells dog treats. The company's fixed and variable costs are modeled by the function C(x)=1.4x+2000. Their revenue is
Naya [18.7K]

<u>Answer:</u>

<u>20,000 packages.</u>

<u>Step-by-step explanation:</u>

The rest of the question is as following:

If x represents the number of packages of dog treats, how many packages do they have to sell to break even? Round your answer to the nearest whole number, and do not include units.

=========================================

The function of fixed and variable costs ⇒ C(x) = 1.4x + 2000

The function of revenue ⇒ R(x) = 1.5x

The even situation will happen when costs = revenue

∴ C(x) = R(x)

∴ 1.4 x + 2000 = 1.5x

Solve for x:

∴ 1.5x - 1.4x = 2000

∴ 0.1 x = 2000

∴ x = 2000/0.1 = 20,000

The even will happen when they sell <u>20,000</u> packages

So, To break even, they have to sell more than 20,000 packages .

3 0
3 years ago
The shop declare a discount of 20% and later a discount of 15% after
Oksi-84 [34.3K]
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Hope this helps!
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Find the slope of the line that goes through the points<br> (12,-14) and (3,-12)<br> Slope, m=
vova2212 [387]

Answer:

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Step-by-step explanation:

The slope is found by

m= (y2-y1)/(x2-x1)

   = (-12- -14)/(3-12)

    =(-12+14)/(3-12)

    =2/-9

   = -2/9

5 0
3 years ago
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