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
Ā crime investigation shows with a new family-oriented comedy show
- There are 400 viewers
ā“ The sample size is 400
- 250 of them indicated they would watch the new show and
Ā suggested it replace the crime investigation show
ā“ The number of success is 250
āµ The population proportion P' = number of success/sample size
ā“ 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
Ā proportion
āµ The confidence interval (CI) = [tex]P'(+/-)z*(\sqrt{\frac{P'(1-P')}{n}}[/tex],
Ā where P' is the sample proportion, n is the sample size, and z*
Ā is the value from the standard normal distribution for the desired
Ā confidence level
āµ 95% z is 1.96
ā“ z* = 1.96
āµ P' = 0.625
āµ n = 400
āµ [tex]\sqrt{\frac{P'(1-P')}{n}}=\sqrt{\frac{0.625(1-0.625)}{400}}=0.0242[/tex]
ā“ CI = 0.625 Ā± (1.96)(0.0242)
ā“ CI = (0.625 - 0.047 , 0.625 + 0.047)
ā“ CI = (0.578 , 0.672)
b) The confidence interval is (0.578 , 0.672)
