Question

a) An adviser in student services would like to estimate the average monthly car payment of all IRSC students. From past research, it is known that the standard deviation of the distribution of all IRSC student car payments is $44. Determine the sample size necessary such that the margin of error of the estimate for a 99% confidence interval for the average monthly car payment of all IRSC students is at most $7.23. Round the solution up to the nearest whole number.

n=

b) A public health official in St. Lucie county needs to estimate the average diastolic blood pressure of all residents in St. Lucie county for a report that is being prepared for the Florida Department of Health.

The official randomly selected 142 St. Lucie county residents and found that the mean diastolic blood pressure of the sample was 80 millimeters of mercury (mm Hg).

Using a 98% confidence level, determine the margin of error, EE, and a confidence interval for the mean diastolic blood pressure of all St. Lucie county residents. From past research, it is known that the standard deviation of the distribution of all St. Lucie county residents' diastolic blood pressure is 9 mm Hg.

Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary.

The margin of error is given by E=.

A 98% confidence interval is given by ______

c)

A musicologist is currently writing a report about pop songs in the late 2010s. As a part of her research, the musicologist would like to estimate the mean length of pop songs in the late 2010s. A random sample of 191 pop songs from the 2010s was selected and the average of the sample was found to be 3.14 minutes with a standard deviation of 0.3 minutes.

Find three different confidence intervals - one with a 98% confidence level, one with a 97% confidence level, and one with a 90% confidence level - for the average length of all pop songs in the late 2010s. Notice how the confidence level affects the margin of error and the width of the interval.

Report confidence interval solutions using interval notation. Round solutions to three decimal places, if necessary.

• The margin of error for a 98% confidence interval is given by E=.
  
  A 98% confidence interval is given by .  
  
• The margin of error for a 97% confidence interval is given by E=.
  
  A 97% confidence interval is given by .  
  
• The margin of error for a 90% confidence interval is given by E=.
  
  A 90% confidence interval is given by .  

Answer 1

Note : Allowed to solve one question per post.

a) An adviser in student services would like to estimate the average monthly car payment of all IRSC students. From past research, it is known that the standard deviation of the distribution of all IRSC student car payments is $44. Determine the sample size necessary such that the margin of error of the estimate for a 99% confidence interval for the average monthly car payment of all IRSC students is at most $7.23. Round the solution up to the nearest whole number.

b) A public health official in St. Lucie county needs to estimate the average diastolic blood pressure of all residents in St. Lucie county for a report that is being prepared for the Florida Department of Health.

The official randomly selected 142 St. Lucie county residents and found that the mean diastolic blood pressure of the sample was 80 millimeters of mercury (mm Hg).

Using a 98% confidence level, determine the margin of error, EE, and a confidence interval for the mean diastolic blood pressure of all St. Lucie county residents. From past research, it is known that the standard deviation of the distribution of all St. Lucie county residents' diastolic blood pressure is 9 mm Hg.

Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary.

The margin of error is given by E=.

A 98% confidence interval is given by ______