Practice with Margin of Error Terms of Use    Contact Person: Donna Roberts

1.
When working with the sampling distribution of a sample statistic, which of the choices would decrease the margin of error?
Choose:
 Increase the sample size. Decrease the sample size. Increase the standard error. Increase the standard deviation.

2.
In an ecological study, the sampling mean proportion is 0.28 and the sample size is 50.
a) What is the margin of error with a confidence level of 95%?

Choose:
 0.028 0.063 0.014 0.127

b)
The researchers are 95% confident that the interval ____________ includes plausible values for the true proportion.
Choose:
 0.22 < p < 0.78 0.15 < p < 0.41 0.22 < p < 0.43 0.31 < p < 0.25

3.
Which choice is the margin of error, with a confidence level of 95%, for estimating the proportion of green mini M&Ms in a container, if 21 green mini M&Ms were drawn from the container in a random sample of 100 M&Ms?
Choose:
 0.041 0.081 0.21 0.105

4.
A researcher works on a study that has a population standard deviation of 0.73, a sample mean of 84.5, and a sample size of 60.
a) What is the margin of error with a confidence level of 95%?
Choose:
 0.109 0.094 0.188 0.07
b) The researcher is 95% confident that the interval ____________ includes plausible values for the true mean.
Choose:
 84.39 < μ < 84.61 84.31 < μ < 84.69 84.43 < μ < 84.57 84.41 < μ < 84.59

5.
Situation: Times between use of TV remote by males during commercials.
• 95% confidence level
n = 25
= 5.25 seconds
• population normally distributed
σ = 2.50 seconds
Which choice is the margin of error in this situation?
Choose:
 0.5 1.05 1 2.1

 6 A drug company is testing a new cold medication for children. The average child's cold symptoms last for 7 days. The company tested 500 children with a cold and found that 250 of them shortened their cold symptoms when taking the new drug. Assuming this to be a random sampling, would it be reasonable for the company to state that half of the children with a cold can decrease the lengths of their symptoms if they take this new drug? Explain.

 7 A study randomly surveyed 1,000 teenagers to determine if they had a TV in their bedroom. Surprisingly, 642 teens responded that they had a TV in their room. a) Find a 95% confidence interval for the proportion of all teens who have a TV in their room. b) If you change the confidence level to 90% (instead of 95%) explain how the confidence interval would change.

 8 A sample data set, n = 110, shows human body temperatures with a mean of 98.4ºF. If the standard deviation σ is known to be 0.65ºF, a) find the margin of error for a 95% confidence level b) find the confidence interval for μ.

 9 Your guidance counselor informs you that a study shows that the average starting salary of college graduates who have taken a statistics course is \$55,785. There were 35 people in the study and the standard deviation σ was \$10,000. For a 95% confidence level, find the confidence interval for this study.

 10 A sample of 60 bottlenose dolphins has a mean weight of 824 pounds. Assuming that σ is known to be 450 pounds, find a 99% confidence interval estimate of the mean of the population of all such dolphin weights.

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