BUSI 230 HW 8.3 Confidence Intervals for a Population Proportion Assignment solutions answers

BUSI 230 HW 8.3 Confidence Intervals for a Population Proportion Assignment solutions complete answers 

 

Just put your values given and automatically provide answers for you!

 

If  is the sample proportion and  is the sample size, then  is the

To estimate the necessary sample size when no value of is available, we use .

 

For the given confidence level and values of  and , find the following.

x=47, n=96, confidence level 99%

(a) Find the point estimate. Round the answers to at least four decimal places, if necessary.

(b) Find the standard error. Round the answers to at least four decimal places, if necessary.

(c) Find the margin of error. Round the answers to at least four decimal places, if necessary.

 

Use the given data to construct a confidence interval for the population proportion  of the requested level.

The confidence interval is

 

Smart phone: Among 241 cell phone owners aged 18-24 surveyed, 104 said their phone was an Android phone.

(a) Find a point estimate for the proportion of smartphone owners aged - who have an Android phone. Round the answer to at least three decimal places.

(b) Construct a 90% confidence interval for the proportion of smartphone owners aged - who have an Android phone. Round the answers to at least three decimal places.

(c) Assume that an advertisement claimed that  of smartphone owners aged - have an Android phone. Does the confidence interval contradict this claim?

 

Sleep apnea: Sleep apnea is a disorder in which there are pauses in breathing during sleep. People with this condition must wake up frequently to breathe. In a sample of 434 people aged 65 and over, 106 of them had sleep apnea.

(a) Find a point estimate for the population proportion of those aged  and over who have sleep apnea. Round the answer to at least three decimal places.

(b) Construct a 99.8% confidence interval for the proportion of those aged  and over who have sleep apnea. Round the answer to at least three decimal places.

(c) In another study, medical researchers concluded that more than  of elderly people have sleep apnea. Based on the confidence interval, does it appear that more than  of people aged  and over have sleep apnea? Explain.

 

LoL: In the computer game League of Legends, some of the strikes are critical strikes, which do more damage. Assume that the probability of a critical strike is the same for every attack and that attacks are independent. Assume that a character has 241 critical strikes out of 596 attacks.

(a) Construct an 80% confidence interval for the proportion of strikes that are critical strikes. Round the answers to at least three decimal places.

(b) Construct a 99.9% confidence interval for the proportion of strikes that are critical strikes. Round the answers to at least three decimal places.

(c) What is the effect of increasing the level of confidence on the width of the interval?

 

Contaminated water: In a sample of 40 water specimens taken from a construction site, 28 contained detectable levels of lead.

(a) Construct an 80% confidence interval for the proportion of water specimens that contain detectable levels of lead. Round the answers to at least three decimal places.

(b) Construct a 99.9% confidence interval for the proportion of water specimens that contain detectable levels of lead. Round the answers to at least three decimal places.

(c) What is the effect of increasing the level of confidence on the width of the interval?

 

Call me: A sociologist wants to construct a 99% confidence interval for the proportion of children aged - living in New York who own a smartphone.

(a) A survey by the National Consumers League estimated the nationwide proportion to be 0.40. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.02?

(b) Estimate the sample size needed if no estimate of p is available.

(c) If the sociologist wanted to estimate the proportion in the entire United States rather than in New York, would the necessary sample size be larger, smaller, or about the same? Explain.

 

How's the economy? A pollster wants to construct an 80% confidence interval for the proportion of adults who believe that economic conditions are getting better.

(a) A poll taken in July  estimates this proportion to be 0.4. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.03?

(b) Estimate the sample size needed if no estimate of p is available.