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MaRussiya [10]
3 years ago
12

A survey of 80 homes in a Washington D.C. suburb showed that 45 were air conditioned. A sample of 120 homes in a Pittsburgh subu

rb showed tht 63 had air conditioning. At α = 0.05, is there a difference in the two proportions? Please show all 4 steps of the classical approach clearly.
Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
5 0

Answer:

There is no significant difference between the two proportions

Step-by-step explanation:

State the hypotheses:

Null hypothesis -> H0: P1 = P2

Alternative hypothesis -> H1: P1 not = P2

Note that hypotheses constitute a two-tailed test. the null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.

Formulate an analysis plan

For the analysis, the significance level is 0.05. The test method is a two-proportion z-test.

Analyze sample data.

Using sample data we calculate the pooled sample porportion (p) and the standard error (SE). Using those measures, we compute the  z-score test statistic (z).

p = (p1*n1 + p2*n2)/(n1 + n2)

p1 = 45/80 = 0.5625

p2 = 63/120 = 0.525

n1 = 80

n2 = 120

p = (0.5625*80 + 0.525*120)/(80 + 120)

p = 0.54

SE = \sqrt{p*(1-p)*(\frac{1}{n_{1} } +\frac{1}{n_{2}} )}

SE = \sqrt{(0.2428)*(0.0125 + 0.0083)}

SE = 0.07112

z = (p1 - p2)/ SE

z = (0.5625 - 0.525)/0.07112

z = 0.527

For z = 0.527 we have p-value 0.198

Interpret results. Since p - Value (0.198) of the test is greater than the alpha-0.05 (For two tailed test α-0.025). Therefore we cannot reject the null hypothesis.

There is no significant difference between the two proportions

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8 - 15 = -7

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2 years ago
2x+3(x-4)=4(2x+3) solving one linear equation form
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Answer:

x= -8

Step-by-step explanation:

2x+3x-12=8x+12

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2 years ago
For 300 trading​ days, the daily closing price of a stock​ (in $) is well modeled by a Normal model with mean ​$196.99 and stand
KATRIN_1 [288]

Answer:

a) 2.5% b) 84% c) 95% d) D. The more unusual day is if the stock closed below $185 because it has the largest absolute z-score.

Step-by-step explanation:

For a) b) and c) we will use the empirical rule, so, we can observe the image shown below

a) 211.23 is exactly two standard deviation above the mean, so, the probability that on a randomly selected day in this period the stock price closed above 211.23 is 2.35% + 0.15% = 2.5%  

b) 204.11 represents exactly one standard deviation above the mean, so, the probability of being below 204.11 is 50% + 34% = 84%

c) The probability of getting a value between 182.75 and 211.23 is 95%, this because 182.75 is exactly two standard deviations below the mean and 211.23 is exactly two standard deviations above the mean.

d) The z-score related to 208 is z_{1} = (208-196.99)/7.12 = 1.5 and the z-score related to 185 is  z_{2} = (185-196.99)/7.12 = -1.7, therefore, the more unusual day is if the stock closed below $185 because it has the largest absolute z-score.

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3 years ago
I'll give brainliest to whoever answers the question correctly!!!
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Is it statement 1 because statement 1 looks out of place.

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M is the midpoint of AD. Triangles A B M and D C M are connected at point M. Sides A B and C D are congruent. The lengths of sid
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Answer:

<h2>Reflection.</h2>

Step-by-step explanation:

The image attached shows a representation of the problem, there you can observe the congruence between triangles.

Also, using the images you can easily deduct the transformation we need to map one triangle onto the other one, we just need to reflect one triangle across and axis that pass through point M, such line acts like a mirror.

Therefore, the right answer is reflection.

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3 years ago
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