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MariettaO [177]

3 years ago

12

The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy sh

ow. Before a final decision is made, network executives commission a sample of 400 viewers. After viewing the comedy, 250 indicated they would watch the new show and suggested it replace the crime investigation show.
(a) Estimate the value of the population proportion. (Round your answer to 3 decimal places.)

Estimated population proportion

(b)
Develop a 95 percent confidence interval for the population proportion. (Round your answers to 3 decimal places.)

1 answer:

tamaranim1 [39]3 years ago

5 0

Answer:

a) The population proportion is 0.625

b) The confidence interval is (0.578 , 0.672)

Step-by-step explanation:

* Lets explain how to solve the problem

- The Fox TV network is considering replacing one of its prime-time

crime investigation shows with a new family-oriented comedy show

- There are 400 viewers

∴ The sample size is 400

- 250 of them indicated they would watch the new show and

suggested it replace the crime investigation show

∴ The number of success is 250

∵ The population proportion P' = number of success/sample size

∴ P' = 250/400 = 0.625

a) The population proportion is 0.625

* Lets solve part b

- Develop a 95 percent confidence interval for the population

proportion

∵ The confidence interval (CI) = $P'(+/-)z*(\sqrt{\frac{P'(1-P')}{n}}$ ,

where P' is the sample proportion, n is the sample size, and z*

is the value from the standard normal distribution for the desired

confidence level

∵ 95% z is 1.96

∴ z* = 1.96

∵ P' = 0.625

∵ n = 400

∵ $\sqrt{\frac{P'(1-P')}{n}}=\sqrt{\frac{0.625(1-0.625)}{400}}=0.0242$

∴ CI = 0.625 ± (1.96)(0.0242)

∴ CI = (0.625 - 0.047 , 0.625 + 0.047)

∴ CI = (0.578 , 0.672)

b) The confidence interval is (0.578 , 0.672)

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