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ad-work [718]
2 years ago
12

A large furniture company claims that 65% of all individuals who buy chairs from its stores choose wood chairs, 20% choose plast

ic chairs, and 15% choose metal chairs. to investigate this claim researchers collected data from a random sample of the companys customers. the results were 305 wood, 121 plastic, and 74 metal. are the data from the sample consistent with the companys claim? conduct an appropriate statistical test at the 5% significance level to support your conclusion make sure to include parameters, check conditions, and show calculations before formulating a conclusion.
Mathematics
2 answers:
Nataly [62]2 years ago
4 0

Answer:

In the sample, 61% chose wooden chairs (4% less than that claimed by the company), 24.2% chose plastic chairs (4.2% more than that claimed by the company), and 14.8 % chose metal chairs (0.2% less than what the company claimed). Therefore, given that these are differences of less than 5%, we can affirm that these samples are consistent with what the company said.

Step-by-step explanation:

Given that a large furniture company claims that 65% of all individuals who buy chairs from its stores choose wood chairs, 20% choose plastic chairs, and 15% choose metal chairs, and to investigate this claim researchers collected data from a random sample of the companys customers, whose results were 305 wood, 121 plastic, and 74 metal, to determine if the data from the sample consistent with the companys claim the following calculations should be performed:

305 + 121 + 74 = 500

500 = 100

305 = X

305 x 100/500 = X

30,500 / 500 = X

61 = X

500 = 100

121 = X

121 x 100/500 = X

12,100 / 500 = X

24.2 = X

100 - 61 - 24.2 = X

39 - 24.2 = X

14.8 = X

Therefore, in the sample, 61% chose wooden chairs (4% less than that claimed by the company), 24.2% chose plastic chairs (4.2% more than that claimed by the company), and 14.8 % chose metal chairs (0.2% less than what the company claimed). Therefore, given that these are differences of less than 5%, we can affirm that these are samples that are consistent with what the company said.

jok3333 [9.3K]2 years ago
4 0

Answer:

The Chi^2 value is 5.654. The p-value is .05919. The result is not significant at p < .05.

Step-by-step explanation:

To do this we need to do a goodness of fit chi-test

You can do it by hand or use a graphing calculator, but IMO using a calculator online is the easiest. Remember one sample is frequency while the other is in proportions so convert one to the other.

In other words if you're doing a proportions test divide 305/500 to get 0.61 and then plug that in next to the expected value of 0.65.

If you/re doing a frequency test, multiply 61% * 5 =325 and then plug that in next to 305.

Both a frequency and a proportion test will yield the same result so don't worry about which you choose.

Once you've plugged the values in you'll get a response like this:

The Chi^2 value is 5.654. The p-value is .05919. The result is not significant at p < .05.

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Viefleur [7K]

Answer:

a)

x(t) = ( 4.167 t + 0.2 cos (2πt))

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b) the  foot have to be 3.32 rev/sec faster

Step-by-step explanation:

Given that:

the speed of the bike = 15 km/hr = 15 × 1000/3600 (m/sec) = 4.167 m/sec

radius of the circle when the foot moves = 20 cm = 0.2 m

radius of the circle above the ground = 30 cm = 0.3 m

Let assume that:

x(t)  should represent the vector along the horizontal moment

y(t) should be the vector along the vertical moment

The initial component will be ( 0, 0.3)

We know that the radius of the circle is given as 0.2 m, So the vector of the circle can be written as (0.2 cos t , 0.2 sin t )

Also, the foot makes one revolution in a second, definitely the frequency of the revolution = 1 and the vector for the circle is ( 0.2 cos (2πt), -0.2 sin  (2πt)), due to the fact that the foot moves clockwise.

Thus, adding all the component together ; we have:

(x(t), y(t)) = (0,0.3)+(4.167 t , 0)+(0.2 cos (2πt), -0.2 sin  (2πt))

(x(t), y(t)) = (4.167 t + 0.2 cos (2πt), 0.3 - 0.2 sin  (2πt))

Hence; the parametric equations are:

x(t) = ( 4.167 t + 0.2 cos (2πt))

y(t) = ( 0.3 - 0.2 sin  (2πt))

b)

The linear speed of rotation is :

15km/hr = 15 × 100, 000/3600 (cm/sec)

             = 416.7 cm/sec

The rotational frequency is :

= 416.7/2πr

= 416.7/2(3.14 × 20)

= 3.32 rev/sec

Hence, the  foot have to be 3.32 rev/sec faster in rotating if an observer standing at the side of the road sees the light moving backward.

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Answer:

B is correct. Your starting amount is 210$ And you're taking away 15$ each time she uses the club,x.

Step-by-step explanation:

Answer:

The linear function model the situation is b = 210 - 15x .

Option (B) is correct .

Step-by-step explanation:

Let us assume that the number of times giselle uses the club be x .

As given

giselle pays $210 in advance on her account at the athletic club.

Each time she uses the club,$15 is deducted from the account.

Let suppose that the money left after giselle uses the club x times is b .

Than the equation becomes

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