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Zepler [3.9K]
3 years ago
13

Suppose that n units are randomly sampled and x number of the sampled units are found to have the characteristic of interest. A

survey of n = 540 pet owners revealed that x = 243 buy their pets holiday presents. For p = proportion of pet owners who revealed that they buy their pets holiday presents, provide a point estimate of p and determine its 95% error margin. Carry out all calculations exactly, round the final answers only. Point estimate =
Mathematics
1 answer:
Ulleksa [173]3 years ago
4 0

Answer:

The point estimate is 0.45.

The 95% error margin is 0.042 = 4.2 percentage points.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is given by:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

Point estimate

We have that n = 540, x = 243

So the point estimate is:

\pi = \frac{243}{540} = 0.45

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

Error margin:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

M = 1.96\sqrt{\frac{0.45*0.55}{540}}

M = 0.0420

The 95% error margin is 0.042 = 4.2 percentage points.

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A tin is a right circular cylinder with a diameter of 6 meters and a height of 10 meters. What is the surface area of this tin,
Alex777 [14]

Answer:

245.04

Step-by-step explanation:

A=2πrh+2πr2=2·π·3·10+2·π·32≈245.04423

Divide 6 by 2 to find the radius

5 0
3 years ago
Identify an equation that models the situation and find its solution. Kane planned to build a 53-centimeter-tall model of a buil
alex41 [277]

Answer:

The increment in the model is 106cm

Step-by-step explanation:

Given

Initial\ Height = 53cm

Final\ Height = 159cm

Required

Determine the increment

To do this, we simply subtract the initial height of the building from the final height

Increment = Final\ Height - Initial\ Height

Increment = 159cm - 53cm

Increment = 106cm

<em>Hence, the increment in the model is 106cm</em>

7 0
3 years ago
State the appropriate null and alternate hypothesis
Nezavi [6.7K]
The null hypothesis states that a population parameter is equal to a hypothesized value. the alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis
4 0
3 years ago
Can someone help me on number one and 4? Thanks! :)
BabaBlast [244]

Answer:

Step-by-step explanation:

I’m pretty sure it’s b

3 0
3 years ago
A box has five items, three good and two defective. three items are selected at random without replacement. let x be the number
user100 [1]
This problem can be solved from first principles, case by case.  However, it can be solved systematically using the hypergeometric distribution, based on the characteristics of the problem:
- known number of defective and non-defective items.
- no replacement
- known number of items selected.

Let
a=number of defective items selected
A=total number of defective items
b=number of non-defective items selected
B=total number of non-defective items
Then 
P(a,b)=C(A,a)C(B,b)/C(A+B,a+b)
where 
C(n,r)=combination of r items selected from n,
A+B=total number of items
a+b=number of items selected

Given:
A=2
B=3
a+b=3
PMF:
P(0,3)=C(2,0)C(3,3)/C(5,3)=1*1/10=1/10
P(1,2)=C(2,1)C(3,2)/C(5,3)=2*3/10=6/10
P(2,0)=C(2,2)C(3,1)/C(5,3)=1*3/10=3/10
Check: (1+6+3)/10=1 ok
note: there are only two defectives, so the possible values of x are {0,1,2}

Therefore the 
PMF:
{(0, 0.1),(1, 0.6),(2, 0.3)}

7 0
3 years ago
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