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aev [14]
3 years ago
7

A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 adult Americans an

d 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
Mathematics
1 answer:
Liula [17]3 years ago
6 0

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 .

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