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A sample of 250 adults tried the new multigrain cereal "Wow!" A total of 187 rated it as excellent. In a sample of 100 children, 66 rated it as excellent. Using the 0.1 significance level, the researcher wishes to show that adults like the cereal better than children. What is the pooled proportion?

(A) 0.723
(B) 1.408
(C) 0.494
(D) 0.807

Respuesta :

JeanaShupp

Answer: (A) 0.723

Step-by-step explanation:

Let X be the number of adults and the number of children tried the new multigrain cereal.

As per given , we have

[tex]X_1=187[/tex]  [tex]X_2=66[/tex]

[tex]n_1=250[/tex]  [tex]n_2=100[/tex]

The pooled proportion = [tex]p=\dfrac{X_1+X_2}{n_1+n_2}[/tex] , where [tex]n_1, n_2[/tex] are different sample sizes.

Put the above values , we get

[tex]p=\dfrac{187+66}{250+100}[/tex]

[tex]p=\dfrac{253}{350}\approx0.723[/tex]

Hence, the pooled proportion= 0.723

Therefore , the correct answer is (A) 0.723 .

Using it's concept, it is found that the pooled proportion is given by:

(A) 0.723

A proportion is the number of desired outcomes divided by the number of total outcomes.

In this problem:

  • In total, 250 + 100 = 350 people were surveyed.
  • Of those, 187 + 66 = 253 rated it as excellent.

Hence, the pooled proportion is:

[tex]p = \frac{253}{350} = 0.723[/tex]

Which means that option A is correct.

A similar problem is given at https://brainly.com/question/24372153

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