Question

A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond​ yes, is approximately​ normal, how many more adult Americans does the researcher need to sample in the following​ cases?

(a) 20% of all adult Americans support the changes(b) 25% of all adults Americans support the changes

Answer 1

Answer:

Adult required in the case of “a” 28 and in the case of “b” the adult requirement is 19.

Step-by-step explanation:

(a) The percentage of adult that support the change is 20 percent.

Now calculate the number of adult required.

Given p = 0.20

Use the below condition:

$np(1 – p) \geq 10 \\n \times 0.20 (1 – 0.20) = 10 \\n = 63 round off$

Since 35 adults are already there so required adults are 63 -35 = 28

(b) The percentage of adult that support the change is 25 percent.

Now calculate the number of adult required.

Given p = 0.25

Use the below condition:

$np(1 – p) \geq 10 \\n \times 0.25 (1 – 0.25) = 10 \\n = 54 (round off)$

Since 35 adults are already there so required adults are 54 -35 = 19 .

Answer 2

Answer:

(A) Researcher need 28 more adult Americans.

(B) Researcher need 19 more adult Americans.

Step-by-step explanation:

Given information:

In both the cases the sample is of 35 Americans is taken and asked if they support the proposed changes or not.

We need to find how many more adult Americans more needed.

(A) 20% of all adults Americans support the changes

So, $p=0.20$

As,

$n \times p(1-p)=10\\\\n \times 0.20(1-020)=10\\n=63$

35 Americans are already in sample then required will be,

$=63-35\\=28$

Hence ,Researcher need 28 more adult Americans.

(B) 25% of all adults Americans support the changes

So, $p=0.25$

As,

$n \times p(1-p)=10\\\\n \times 0.25(1-025)=10\\n=54$

35 Americans are already in sample then required will be,

$=54-35\\=19$

Hence ,Researcher need 19 more adult Americans.

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