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oksano4ka [1.4K]
3 years ago
10

The manager of Petco, a nationwide chain of pet supply stores, wants to study characteristics of the customers, particularly the

amount of money spent by customers and whether the customers own only one dog, only one car, or more than on dog and/or cat. The results from a sample of 70 customers are as follows: Amount of money spent: LaTeX: X-bar\:=\:\text{21.34}X − b a r = 21.34 LaTeX: S\:=\:\text{9.22}S = 9.22 Thirty-seven customers own only a dog. Twenty-six customers own only a cat. Seven customers own more than one dog and/or cat. Construct a 95% confidence interval estimate for the population mean amount spent in the pet supply store.
Mathematics
1 answer:
shutvik [7]3 years ago
3 0

Answer:

The 95% confidence interval would be given by (19.141;23.538)  

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X=21.34 represent the sample mean for the sample  

\mu population mean (variable of interest)

s=9.22 represent the sample standard deviation

n=70 represent the sample size  

2) Confidence interval

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=70-1=69

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,69)".And we see that t_{\alpha/2}=1.994

Now we have everything in order to replace into formula (1):

21.74-1.994\frac{9.22}{\sqrt{70}}=19.141    

21.74+1.994\frac{9.22}{\sqrt{70}}=23.538

So on this case the 95% confidence interval would be given by (19.141;23.538)    

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Answer:

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Step-by-step explanation:

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7 0
2 years ago
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Dmitry [639]

Answer:

Rounding it to two decimal places, we get distance, d=17.35

Step-by-step explanation:

Given:

The two points are (9.7, -2.8)\textrm{ and }(-3.2, 8.8)

The distance between the two points can be obtained using the distance formula which is given as:

d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}

Here, for the points, (9.7, -2.8)\textrm{ and }(-3.2, 8.8)

x_{1}=9.7,x_{2}=-3.2,y_{1}=-2.8,y_{2}=8.8

Therefore, the distance between the points is:

d=\sqrt{(-3.2-9.7)^2+(8.8-(-2.8))^2}\\d=\sqrt{(-12.9)^2+(8.8+2.8)^2}\\d=\sqrt{(12.9)^2+(11.6)^2}\\d=\sqrt{166.41+134.56}\\d=\sqrt{300.97}=17.348

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7 0
3 years ago
Round your answer to the nearest hundredth BC=?
miskamm [114]

Answer:

BC = 1.71

Step-by-step explanation:

well to start we have to know the relationship between angles, legs and the hypotenuse  in a right triangle

α = 70°

a: adjacent  = BC

h: hypotenuse = 5

sin α = o/h

cos α= a/h

tan α = o/a

we see that it has (angle, adjacent, hypotenuse)

we look at which meets those data between the sine, cosine and tangent

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0.34202 = a/5

0.34202 * 5 = a

1.7101 = a

round to the neares hundredth

a = 1.7101 = 1.71

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7 0
2 years ago
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Margarita [4]
I believe the shirts are different (in color, in size, in style,...), is so then:

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6 0
3 years ago
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WITCHER [35]
Answer:
(assuming this isn't actually for math?) but one reason is bc science shouldn't be always taken as fact. science can be wrong.

Explanation:
not all but many scientists are skeptical and won't accept anything without proof, and even when things are accepted as right they can still be wrong later. example: humans once believed the planets revolved around the earth and that the earth was flat (even, some people still believe the earth is flat today....) but both those things are generally unaccepted today.

science shouldn't be viewed as fact always, because accepting everything as fact will lead to misassumptions and false information. it's like we should never take things for granted
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