Estimating a Population Mean

The makers of a specialty brand of bottled water claim that their “mini” bottles contain 8 ounces of water. To investigate this claim, a consumer advocate randomly selected a sample of 10 bottles and carefully measured the amount of water in each bottle. The mean volume was 7.98 ounces and the 95% confidence interval for true mean volume is 7.93 to 8.03 ounces. Based on the sample, which of the following conclusions best addresses the makers’ claim?

• Because 7.98 is in the interval, there is convincing evidence that their claim is correct.

• Because 7.98 is in the interval, there is not convincing evidence that their claim is incorrect.

• Because 8 is in the interval, there is convincing evidence that their claim is correct.

• Because 8 is in the interval, there is not convincing evidence that their claim is incorrect.

• Because 0 is not the interval, there is convincing evidence that their claim is incorrect.

The weights (in pounds) of three adult males are 160, 215, and 195. What is the standard error of the mean for these data?

• 190

• 27.84

• 22.73

• 16.07

• 13.13

A 90% confidence interval for the mean μ of a population is computed from a random sample and is found to be 90 ± 30 . Which of the following could be the 95% confidence interval based on the same data?

• 90 ± 21

• 90 ± 30

• 90 ± 39

• 90 ± 70

• Without knowing the sample size, any of the above answers could be the 95% confidence interval.

A researcher was interested in comparing the salaries of employees of a particular company that work in the HR and IT departments. Independent random samples of 8 HR employees and 15 IT employees yielded the weekly salaries shown in the table (in dollars). Construct a 98% confidence interval estimate of the difference in population mean weekly salary.

• (-$385, $164)

• (-$158, $382)

• (-$335, $111)

• (-$431, $208)

• (-$382, $158)

A research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend exercising each week. They want to estimate the mean within a margin of error of 0.5 hours with a 95% level of confidence. Previous data suggests that the standard deviation of the population is 2.2. Which of the following is the smallest sample size they could use?

• 60

• 75

• 90

• 180

In a sample of 50 people in a town, the average yearly consumption of fruits is found to be 75 kilograms with a margin of error of 10 kilograms. Estimate the total yearly consumption of fruits in kilograms for the town's population of 2000 people.

• 130,000 kg-170,000 kg

• 110,000 kg-120,000 kg

• 180,000 kg- 200,000 kg

• 130 kg- 170 kg

A survey of 200 students at a high school finds that the average amount of money spent on lunch per week is $25 with a margin of error of ±5. Estimate the total amount of money spent by all students at the high school on lunch per week if there are 1200 students.

• $15,000-$20,000

• $24,000-$36,000

• $770

• $40,000

• 50

• 25

• 20

• 5

If the mean of a sample is 203 and the margin of error is 4.6, what would be a reasonable mean for the population?

• 99.2

• 198.3

• 207.2

• 207.7

Do you expect that this mean of 5 is the same as the true population mean?

• Yes

• No