BUSI 230 HW 7.3, HW 7.4, HW 8.1, HW 8.2, HW 8.3 Connect Exercises Week 5 solutions complete answers

BUSI 230 HW 7.3, HW 7.4, HW 8.1, HW 8.2, HW 8.3 Connect Exercises Week 5 solutions complete answers 

 

BUSI 230 HW 7.3 Sampling Distributions and the Central Limit Theorem Assignment 

 

Select the appropriate word or phrase to complete the sentence.

The probability distribution of  is called a  distribution.

states that the sampling distribution of  is approximately normal when the sample is large.

 

A sample of size 125 will be drawn from a population with mean 50 and standard deviation 17. Use the TI-83 Plus/TI-84 Plus calculator.

(a) Find the probability that x will be greater than 52. Round the final answer to at least four decimal places.

(b) Find the 35 percentile of x. Round the answer to at least two decimal places.

 

A sample of size 190 will be drawn from a population with mean 45 and standard deviation 11. Use the TI-83 Plus/TI-84 Plus calculator.

(a) Find the probability that x will be less than 43. Round the final answer to at least four decimal places.

(b) Find the 60 percentile of x. Round the answer to at least two decimal places.

 

Watch your cholesterol: The mean serum cholesterol level for U.S. adults was 201, with a standard deviation of 40.8 (the units are milligrams per deciliter). A simple random sample of 109 adults is chosen. Use Excel. Round the answers to at least four decimal places.

(a) What is the probability that the sample mean cholesterol level is greater than 208?

(b) What is the probability that the sample mean cholesterol level is between 193 and 199?

(c) Would it be unusual for the sample mean to be less than 195?

 

Taxes: The Internal Revenue Service reports that the mean federal income tax paid in the year 2010 was $8,040. Assume that the standard deviation is $5,000. The IRS plans to draw a sample of 1,000 tax returns to study the effect of a new tax law.

(a) What is the probability that the sample mean tax is less than $7,800? Round the answer to at least four decimal places.

(b) What is the probability that the sample mean tax is between $7,600 and $7,900? Round the answer to at least four decimal places.

(c) Find the 70 percentile of the sample mean. Round the answer to at least two decimal places.

(d) Would it be unusual if the sample mean were less than $7,900? Round the answer to at least four decimal places.

(e) Do you think it would be unusual for an individual to pay a tax of less than $7,900? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places.

 

High-rent district: The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2,676. Assume the standard deviation is $509. A real estate firm samples 108 apartments. Use Excel.

(a) What is the probability that the sample mean rent is greater than $2,746? Round the answer to at least four decimal places.

(b) What is the probability that the sample mean rent is between $2,550 and $2,555? Round the answer to at least four decimal places.

(c) Find the 75 percentile of the sample mean. Round the answer to at least two decimal places.

(d) Would it be unusual if the sample mean were greater than $2,780? Round the answer to at least four decimal places.

(e) Do you think it would be unusual for an individual apartment to have a rent greater than $2,780? Explain. Assume the population is approximately normal. Round the answer to at least four decimal places.

 

Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 46, with a standard deviation of 34. A pollster draws a sample of 90 people to interview.

(a) What is the probability that the sample mean income is less than 41? Round the answer to at least four decimal places.

(b) What is the probability that the sample mean income is between 42 and 47? Round the answer to at least four decimal places.

(c) Find the 20 percentile of the sample mean. Round the answer to at least one decimal place.

(d) Would it be unusual for the sample mean to be less than 34? Round the answer to at least four decimal places.

(e) Do you think it would be unusual for an individual to have an income of less than 34? Explain. Assume the population is approximately normal. Round the answer to at least four decimal places.

 

Liberty University BUSI 230 HW 7.4 The Central Limit Theorem for Proportions Assignment complete solutions answers and more!

 

If  is the sample size and  is the number in the sample who have a certain characteristic, then  is called the sample .

The probability distribution of  is called a  distribution.

 

Below,  is the sample size,  is the population proportion and  is the sample proportion. Use the excel spread sheet to find the probability. Round the answer to at least four decimal places.

 

Coffee: The National Coffee Association reported that 65% of U.S. adults drink coffee daily. A random sample of 250 U.S. adults is selected. Round your answers to at least four decimal places as needed.

(a) Find the mean .

(b) Find the standard deviation .

(c) Find the probability that more than 68% of the sampled adults drink coffee daily.

(d) Find the probability that the proportion of the sampled adults who drink coffee daily is between 0.59 and 0.67.

(e) Find the probability that less than 66% of sampled adults drink coffee daily.

(f) Would it be unusual if less than 61% of the sampled adults drink coffee daily?

 

Smartphones: A poll agency reports that 64% of teenagers aged 12-17 own smartphones. A random sample of 65 teenagers is drawn. Round your answers to at least four decimal places as needed.

(a) Find the mean .

(b) Find the standard deviation .

(c) Find the probability that more than 66% of the sampled teenagers own a smartphone.

(d) Find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.61 and 0.75.

(e) Find the probability that less than 75% of sampled teenagers own smartphones.

(f) Would it be unusual if less than 60% of the sampled teenagers owned smartphones?

 

Working two jobs: About 17% of employed adults in the United States held multiple jobs. A random sample of 50 employed adults is chosen. Use Excel as needed.

(a) Is it appropriate to use the normal approximation to find the probability that less than 6.9% of the individuals in the sample hold multiple jobs? If so, find the probability. If not, explain why not.

(b) A new sample of 115 employed adults is chosen. Find the probability that less than 6.9% of the individuals in this sample hold multiple jobs. Round the answer to at least four decimal places.

(c) Find the probability that more than 6.4% of the individuals in the sample of 115 hold multiple jobs. Round the answer to at least four decimal places.

(d) Find the probability that the proportion of individuals in the sample of 115 who hold multiple jobs is between 0.180 and 0.220. Round the answer to at least four decimal places.

(e) Would it be unusual if less than 15% of the individuals in the sample of 115 held multiple jobs? Round the answer to at least four decimal places.

 

Liberty University BUSI 230 HW 8.1 Confidence Intervals for a Population Mean, Standard Deviation Known Assignment complete solutions answers and more!

 

Fill in the blank with the appropriate word or phrase.

A single number that estimates the value of an unknown parameter is called  estimate.

The margin of error is the product of the standard error and the .

In the confidence interval , the quantity  is called the .

 

Find the critical value  needed to construct a confidence interval with level 92%.

The critical value for the confidence level is

 

A sample of size n=61 is drawn from a population whose standard deviation is =34. Find the margin of error for a  confidence interval for 90%. Round the answer to at least three decimal places.

The margin of error for a  confidence interval for  is .

 

A sample of size n=92 is drawn from a normal population whose standard deviation is =8.3. The sample mean is =38.88.

(a) Construct an 99.5% confidence interval for . Round the answer to at least two decimal places.

(b) If the population were not approximately normal, would the confidence interval constructed in part (a) be valid? Explain.

 

How many computers? In a simple random sample of 170 households, the sample mean number of personal computers was 1.31. Assume the population standard deviation is 0.99.

(a) Construct a  confidence interval for the mean number of personal computers. Round the answer to at least two decimal places.

A  confidence interval for the mean number of personal computers is .

(b) If the sample size were  rather than , would the margin of error be larger or smaller than the result in part (a)? Explain.

(c) If the confidence levels were  rather than , would the margin of error be larger or smaller than the result in part (a)? Explain.

(d) Based on the confidence interval constructed in part (a), is it likely that the mean number of personal computers is less than ?

 

Babies: According to a recent report, a sample of 300 one-year-old baby boys in the United States had a mean weight of 25.5 pounds. Assume the population standard deviation is 5.3 pounds.

(a) Construct a 99.9% confidence interval for the mean weight of all one-year-old baby boys in the United States. Round the answer to at least one decimal place.

(b) Should this confidence interval be used to estimate the mean weight of all one-year-old babies in the United States? Explain.

(c) Based on the confidence interval constructed in part (a), is it likely that the mean weight of all one-year-old boys is greater than  pounds?

 

How smart is your phone? A random sample of  Samsung Galaxy smartphones being sold over the Internet in  had the following prices, in dollars:

(a) Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval.

(b) Following is a dotplot of these data. Is it reasonable to assume that the population is approximately normal?

(c) If appropriate, construct a 95% confidence interval for the mean price for all phones of this type being sold on the Internet in 2013. Round your intermediate step to three decimal places. Round your answer to one decimal place.

 

Liberty University BUSI 230 HW 8.2 Confidence Intervals for a Population Mean, Standard Deviation Unknown Assignment complete solutions answers and more!

 

When constructing a confidence interval for a population mean  from a sample of size 20, the number of degrees of freedom for the critical value  is .

 

Find the critical value  needed to construct a confidence interval of the given level with the given sample size. Round the answer to at least three decimal places.

 

Online courses: A sample of 269 students who were taking online courses were asked to describe their overall impression of online learning on a scale of 1-7, with 7 representing the most favorable impression. The average score was 5.77, and the standard deviation was 0.98.

(a) Construct a 90% interval for the mean score. Round the answers to two decimal places.

(b) Assume that the mean score for students taking traditional courses is . A college that offers online courses claims that the mean scores for online courses and traditional courses are the same. Does the confidence interval contradict this claim? Explain.

 

Get an education: In 2012 the General Social Survey asked 844 adults how many years of education they had. The sample mean was 8.54 years with a standard deviation of 8.58 years.

(a) Construct a 99% interval for the mean number of years of education. Round the answers to two decimal places.

(b) Data collected in an earlier study suggest that the mean in  was  years. A sociologist believes that the mean in  is the same. Does the confidence interval contradict this claim?

 

Sound it out: Phonics is an instructional method in which children are taught to connect sounds with letters or groups of letters. A sample of 136 first graders who were learning English were asked to identify as many letter sounds as possible in a period of one minute. The average number of letter sounds identified was 34.01 with a standard deviation of 23.83.

(a) Construct a 90% interval for the mean number of letter sounds identified in one minute. Round the answers to two decimal places.

(b) If a  confidence interval were constructed with these data, would it be wider or narrower than the interval constructed in part (a)? Explain.

 

Baby weights: Following are weights, in pounds, of  two–month–old baby girls. It is reasonable to assume that the population is approximately normal.

(a) Construct a 90% interval for the mean weight of two-month-old baby girls.

(b) According to the National Health Statistics Reports, the mean weight of two–month–old baby boys is  pounds. Based on the confidence interval, is it reasonable to believe that the mean weight of two–month–old baby girls may be the same as that of two–month–old baby boys? Explain.

 

Sleeping outlier: A simple random sample of eight college freshmen were asked how many hours of sleep they typically got per night. The results were

Notice that one joker said that he sleeps 24 hours a day.

(a) The data contain an outlier that is clearly a mistake. Eliminate the outlier, then construct a 90% confidence interval for the mean amount of sleep from the remaining values. Round the answers to two decimal places.

(b) Leave the outlier in and construct the  confidence interval. Round the answers to two decimal places.

 

Liberty University BUSI 230 HW 8.3 Confidence Intervals for a Population Proportion Assignment complete solutions answers and more!

 

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.