Question

In: Statistics and Probability

The Fox TV network is considering replacing one of its prime-time crime investigation shows with a...

The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 490 viewers. After viewing the comedy, 420 indicated they would watch the new show and suggested it replace the crime investigation show.   

a. Estimate the value of the population proportion. (Round the final answer to 3 decimal places.)

Estimate of proportion           

b. Compute the standard error of the proportion. (Round the final answer to 3 decimal places.)

Standard error of the proportion             

c. Develop a 95% confidence interval for the population proportion. (Round the final answers to 3 decimal places.)

The confidence interval is between  and  .

d. Interpret your findings. (Round the final answers to the nearest whole number.)

We are reasonably sure the population proportion is between  and  %.

------------------------------------------------------------------------------------------------------------------------

A sample of 15 observations is selected from a normal population where the population standard deviation is 12. The sample mean is 47.  

a. Determine the standard error of the mean. (Round the final answer to 3 decimal places.)

The standard error of the mean is  .

b. Determine the 95% confidence interval for the population mean. (Round the z-value to 2 decimal places. Round the final answers to 3 decimal places.)

The 95% confidence interval for the population mean is between  and  .

Solutions

Expert Solution

Solution :

Given that n = 490 , x = 420

a.
=> The population proportion p = x/n = 420/490 = 0.857

=> q = 1 - p = 0.143

b.   
=> The standard error of the proportion = sqrt(p*q/n)

= sqrt(0.857*0.143/490)

= 0.016

c.
=> for 95% confidence interval , Z = 1.96

=> The 95% confidence interval for the population proportion is

=> p +/- Z*sqrt(p*q/n)

=> 0.857 +/- 1.96*0.016

=> (0.8256 , 0.8883)

=> (0.826 , 0.888) (rounded)

=> (82.6% , 88.8%)

=> (83% , 89%) (nearest whole number)

=> The confidence interval is between 0.826 and 0.888   

d. => We are reasonably sure the population proportion is between 83% and 89%

-----------------------------------------------------------------------------------------------

Solution :

Given that n = 15 , population standard deviation σ = 12 , sample mean x-bar = 47

a.
=> The standard error of the mean is = σ/sqrt(n)

= 12/sqrt(15)

= 3.098 (rounded)

b. => for 95% confidence interval , Z = 1.96

=> The 95% confidence interval for the population mean is

=> x-bar +/- Z*σ/sqrt(n)

=> 47 +/- 1.96*3.098

=> (40.9279 , 53.0721)

=> (40.928 , 53.072) (rounded)

=> The 95% confidence interval for the population mean is between 40.928 and 53.072


  


Related Solutions

The Fox TV network is considering replacing one of its prime-time crime investigation shows with a...
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family oriented comedy show. 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 suggested it replace the crime investigation show. For an 84.5% confidence interval, what is the upper confidence limit for the proportion who prefer the new show? Express your sollutions as the decimal equivalent...
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a...
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 440 viewers. After viewing the comedy, 340 indicated they would watch the new show and suggested it replace the crime investigation show.    a. Estimate the value of the population proportion. (Round the final answer to 3 decimal places.) Estimate of proportion            b. Compute the standard error...
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a...
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 350 viewers. After viewing the shows, 250 indicated they would watch the new show and suggested it replace the crime investigation show. Estimate the value of the population proportion. (Round your answers to 3 decimal places.) Population proportion_________? Develop a 99% confidence interval for the population proportion. (Use...
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a...
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. 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 the final answer to 3 decimal places.) Estimate of proportion            b. Compute the standard error...
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a...
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 490 viewers. After viewing the comedy, 420 indicated they would watch the new show and suggested it replace the crime investigation show.    a. Estimate the value of the population proportion. (Round the final answer to 3 decimal places.) Estimate of proportion            b. Compute the standard error...
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a...
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 450 viewers. After viewing the shows, 200 indicated they would watch the new show and suggested it replace the crime investigation show. Estimate the value of the population proportion. (Round your answers to 3 decimal places.) Develop a 98% confidence interval for the population proportion. (Use z Distribution...
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a...
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 500 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 the z-values to 2 decimal places. Round your answer to 3 decimal places.) B) Develop a 90%...
A small café is considering replacing one of its waitstaff with a ‘robot’ – a device...
A small café is considering replacing one of its waitstaff with a ‘robot’ – a device that will take orders, deliver food and interact with customers in an entertaining way. The cost of the robot is $225,000. From the salary savings and the extra customers the robot is expected to attract, it is estimated that the net inflows from the idea will be: • Year 1: $95,100 • Year 2: $80,000 • Year 3: $60,000 • Year 4: $55,000 It...
a) The worksheet "Counts8Year" provides the number Top30 TV shows aired on each network by year....
a) The worksheet "Counts8Year" provides the number Top30 TV shows aired on each network by year. Run a two-way ANOVA without replication using the data in columns A to E of the "Counts8Year" worksheet. (Do not include row 1 and check labels.) Two hypothesis tests will be performed, one for the Year (row) factor and the other for the Network (column) factor. What is the value of the test statistic, Fcalc, for the test on the Network factor? Provide your...
Komatsu Cutting Technologies is considering replacing one of its CNC machines with one that is newer...
Komatsu Cutting Technologies is considering replacing one of its CNC machines with one that is newer and more efficient. The firm purchased the CNC machine 12 years ago at a cost of $132,000. The machine had an expected economic life of 16 years at the time of purchase and an expected salvage value of $13,000 at the end of the 16 years. The original salvage estimate is still good, and the machine has a remaining useful life of 4 years....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT