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) = ,
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
∵
∴ 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)