Margin of Error and Sample Size

For a class project, a student in a statistics class surveys the monthly rent for 32 unfurnished one-bedroom apartments in Boston and finds the mean monthly rent to be $1400 with a standard deviation of $220.

Find the margin of error for the sample mean. (assuming 95% confidence) Round to the nearest hundredth

• $77.78

• $4.31

• $188.78

• $494.97

For a class project, a student in a statistics class surveys the monthly rent for 32 unfurnished one-bedroom apartments in Boston and finds the mean monthly rent to be $1400 with a standard deviation of $220.

Find the 95% confidence interval for the population mean Round to the nearest hundredth

• [1322.22, 1477.78]

• [1395.69, 1404.31]

• [1211.22, 1588.78]

• [905.03, 1894.97]

A random sample of 45 life insurance policy holders showed that the average premiums paid on their life insurance policies was $340 per year with a standard deviation of $62. Construct a 95% confidence interval for the population mean. Round to the nearest hundredth

• [321.52, 358.48]

• [238.63, 441.37]

• [253.64, 426.36]

• [328.57, 351.43]

A survey was conducted where 150 high school students were asked the average amount of time they spent doing household chores in one week. The data collected resulted in a mean time of 180.5 minutes with a standard deviation of 5.5 minutes. Which of these represents a 95% confidence interval for the mean weekly hours spent doing household chores of all high school students?

• [171.5, 189.5]

• [175, 186]

• [178.3, 182.8]

• [179.6, 181.4]

A sample of 121 high school seniors were surveyed on their level of school spirit on a scale of 0-100. The sample mean of this survey is 86. The known population standard deviation is 14 for all seniors in the class. Which of these is a 95% confidence interval for the population mean?

• [82.7, 89.3]

• [83.5, 88.5]

• [83.9, 88.1]

• [85.9, 86.1]

A sample of n students were asked for the average amount of money they spend in a day. The data resulted in a mean of $5.50 with a standard deviation of $2.45. If the margin of error was $0.31, how many students were in the sample? Round to the nearest whole student

• 250

• 16

• 100

• 500

A researcher wishes to estimate, within $25, the true mean amount of postage a community college spends each year. The standard deviation is known to be $80. If she wishes to be 95% confident in her estimate of the true mean amount of postage, how large a sample is necessary? Round to the nearest whole number

• 41

• 25

• 80

• 200

Suppose a department store wants to estimate within 2 years the true mean age of the customers in its contemporary apparel department. The department store manager assumes a standard deviation of 7.5 years. How large a sample is required to estimate the true mean age with 95% confidence?

Round to the nearest whole number

• 56

• 112

• 420

• 224

Researchers want to estimate with 95% confidence the true mean pulse rate of American adult males who jog at least 15 miles per week. They survey 21 males and find the sample mean pulse rate to be 52.6 beats per minute and a standard deviation of 3.22 beats per minute. Find the margin of error for the mean pulse rate of all American adult males who jog at least 15 miles per week. Round to the nearest tenth.

• 1.4 beats per minute

• 1.7 beats per minute

• 0.9 beats per minute

• 4.1 beats per minute

Researchers want to estimate with 95% confidence the true mean pulse rate of American adult males who jog at least 15 miles per week. They survey 21 males and find the sample mean pulse rate to be 52.6 beats per minute and a standard deviation of 3.22 beats per minute. Suppose the researchers want to estimate the mean within 1 beat per minute. How large must the sample size be? Round to the nearest whole number.

• 41

• 21

• 53

• 36