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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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Can anyone solve part C?​
nlexa [21]

Answer:

y - 7 = 4(x - 35)

Step-by-step explanation:

The fundamental theorem of calculus states that:

\frac{d}{dx} \int\limits^x_a {f(t)} \, dt = f(x).

So using the fundamental theorem of calculus, you can find that h'(x) = f(x).

The question tells you that f(x) is periodic with a period of 8, so f(x) repeats itself every 8 units.

Using this, you can find that the slope of h(x) at x = 35 is the same as the slope of h(x) at x = 3, which is 4.

The slope of h(x) at x = 35 is 4.

Now I have to find the value of h(x) when x = 35. It is the area under f(x) from 0 to 35.

The area underneath f(x) from 0 to 35 is 7. When x = 35, h(x) = 7.

Now use the point-slope formula to write the equation of the tangent line.

The answer is <u>y - 7 = 4(x - 35)</u>

3 0
3 years ago
Read 2 more answers
Two lines intersect to form a linear pair with equal measures. One angle had the measure 2x and the other angle had the measure
rosijanka [135]

Answer:

x = 45, y = 5

Step-by-step explanation:

It is given that two lines form a linear pair with equal measures. Therefore, the angle between the two lines will be 90. Now, according to the question,

2x + 20y - 10 =90

2x+20y = 100

x + 10y = 50

And

2x = 20y-10

x = 10y -5

x - 10 y = -5

Now, adding x + 10y = 50 and x - 10y =-5, the value of x can be found. The required value will be:

x + 10y =50

x - 10y = -5

------------------

x = 45

Therefore, the value of y after substitution of the value of x in one of the equations will be:

90 = 20y - 10

20 y = 100

y = 5

Hence, the required value of x and y are 45 and 5 respectively.

4 0
3 years ago
Wegnerkolmp or someone who can explain this to me
netineya [11]

Answer:

m<CDE=66 degrees.

Step-by-step explanation:

(1) Extend the segment DC so it intersects with line BA. Call the intersection F.

(2) Consider triangle BCF. In here, we are given m<ABC=24 deg. Since m<BCD = 90 deg, we known that m<BCF = 90 deg. Knowing two angles in the triangle BCF lets us determine the rhird angle m<BFC = 180-90-24 = 66 deg.

(3) Because of the fact that AB || DE and the fact that line DF intersects AB and DE, the angles <BFC and <CDE are congruent. Therefore m<CDE=66 deg.


3 0
3 years ago
Solve the equation 4n = 9
aliina [53]

Answer:

n = 9/4 = 2.250

Step-by-step explanation:

Rearrange:     4*n-(9)=0

Solve:  4n-9 = 0

     4n = 9

       n = 9/4 = 2.250

answer:     n = 9/4 = 2.250

6 0
3 years ago
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The rule for the number of fish in a home aquarium is 1 gallon of water for each inch of fish length. Marta's aquarium holds 39
Karo-lina-s [1.5K]

Answer: Fish A: 9 inches ; Fish B: 6 inches

Step-by-step explanation:

This can be turned into a systems of equation, where x equals the length of fish A and y equals the length of fish B:

3x + 2y = 39 → -3x - 2y = -39

3x + 4y = 51 → 3x +4y = 51

Combine: 0 + 2y = 12 → y = 6 inches.

Plug back in: 3x + 2(6) = 39 → 3x = 27 → x = 9 inches.

8 0
2 years ago
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