MATHEMATICS

1. Express the confidence interval ( 0.018,0.114) in the form of p-E<p< p+E

 

2. In the week before and the week after a holiday there were 10,000 total deaths, and 4954 of them occurred in the week before the holiday.  (Show work)

a. Construct a 90% confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and the week after the holiday.

b. Based on the result, does there appear to be any indication that people can temporarily postpone their death to survive the hoiday? yes or no

 

3.An online site presented this question, Would the recent norovirus outbreak deter you from taking a cruise?” Among the 34,643 people who responded, 68% answered yes. Use the sample data to construct a 95% confidence interval estimate for the proportion of the population of all who would respond yes to that question. Does the confidence interval provide a good estimate of the population proportion?

 

4. A data set includes 110 body temperatures of healthy adult humans for which x= 98.0 F and s= 0.74F Complete parts a & b (Show work)

a. What is the best point estimate of the mean body temperature of all healthy humans?

 

b. Using the sample statistics, construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. Do the confidence interval limits contain 98.6F? What does the sample suggest avout the use of 98.6F as the meand body temperature?

What is the confidence intercal estimate of the population mean?

___F<u<___F

 

Do the confidence interval limits contain 98.6F yes or no?

 

5. In a sample of seven cars, each car was tested for nitrogen-oxide emissions ( in gram per mile) and the following results were obtained: 0.06, 0.18, 0.11, 0.16, 0.05, 0.05, 0.11. Assuming that this sample is representive of the cars in use, construct a 98% confidence interval estimate of the mean amount of nitrogen-oxide emissions for all cars. If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, can we safely conclude that this requirement is being met?

 

 

What is the confidence interval estimate of the mean amount of nitrogen-oxide emissions for all cars?

___g/mi < u < -___ g / mi (round three decimal places as needed)

 

Can we safely conclude that the requirement that nitrogen-oxide emissions be less than 0.165 g/mi is being met?

 

6. In order to estimate the mean amount of time computer users spend on the internet each month, how many computer users must be surveyed in order to be 90% confident that your sample mean is within 12 minutes of the population mean? Assume that the standard deviation of the population of monthy time spent on the internet is 197 min. What is the major obstacle to getting a good estimate of the population mean? Use technology to find the estimated minimum required sample size.

 

The minimum sample size required is ____computer users.

 

What is the major obstacle to getting a good estimate of the population mean?

a. there may not be 730 computere users

b. The data does note provided information on what the computer users did while on the internet.

c. It is difficult to precisely measure the amount of time spent on the internet invalidating some data values

d. There are no obstacles to getting a good estimate of the population mean

 

7.If we find that there is a linear correlation between the concentration of carbon dioxide in our atmosphere and the global temperature, does that indicate that changes in the concentration of carbon dioxide cause changes in the global temperature?

 

8. For a sample of eight bears researchers measured the distances around the bears chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is r=0.829. Using a=0.05, determine if there is a linear correlation between chest size and weight . What proportion of the variation in weight can be explained by the linear relationship between weight and chest size.

a. Is there a linear correlation between chest and weight?

b. What proportion of the variation in wight can be explained by the linear relationship between weight and chest size?

 

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