You have been asked to calculate a 95% confidence interval for a data sample.
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- You have been asked to calculate a 95% confidence interval for a data sample. You know the mean of this sample but you do not know the population standard deviation. The probability distribution you should use in your calculations is the
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Whatever distribution the data follow.
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Normal Distribution.
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no distribution. You cannot do this problem.
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Student-t Distribution.
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- Using the data below, calculate the 95% confidence interval. Round your answers to two decimal places. What is the lower bound for the confidence interval?
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3.3
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2.9
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3
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3.1
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2.7
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2.6
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4
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3.8
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2.8
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3.6
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- Calculate the 95% confidence interval for the data below. Round your answers to two decimal places. What is the upper bound for the 95% confidence interval?
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3.3
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2.9
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3
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3.1
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2.7
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2.6
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4
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3.8
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2.8
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3.6
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- Calculate a 90% confidence for the data below. Round your answers to two decimal places. What is the lower bound on the 90% confidence interval?
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3.3
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2.9
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3
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3.1
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2.7
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2.6
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4
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3.8
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2.8
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3.6
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- You have been asked to calculate a 90% confidence interval for the data below. Round your answers to two decimal places. What is the upper bound on the 90% confidence interval?
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3.3
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2.9
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3
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3.1
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2.7
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2.6
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4
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3.8
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2.8
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3.6
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- The 90% confidence interval is wider than the 95% confidence interval for the same data because a lower confidence level actually covers more area, i.e. a wider interval.
True
False
- If you increase the number of observations in your dataset you would expect your confidence interval to become narrower.
True
False
- Many students misinterpret a confidence interval, i.e. a 90% confidence interval, to mean that there is confidence that 90% of the data lie within this interval. That is not true. Fill in the blank in the following sentence to complete what is accurately meant in expressing a confidence interval for an analysis involving the true population mean of students' GPA.
We estimate with 90% confidence that ________ lies between the lower bound of the confidence interval and the upper bound of the confidence interval.
- Fill in the blanks in the following sentences about the differences between the Normal distribution and the Student-t distribution.
The Student-t distribution has more
- in its tails than the Normal distribution. You do not need to know the
- standard deviation to use the Student-t distribution. Graphs of the Normal distribution and the Student-t distribution look very similar. However, the exact shape of the Student-t distribution depends on the
- . As the number of degrees of freedom increases the Student-t distribution becomes more and more like the Normal distribution.
- If you have a binomial distribution you are dealing with a proportion problem.
True
False
- What is the proportion of international students in the following data?
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Student
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Undergraduate GPA
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International
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A
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3.3
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No
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B
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2.9
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No
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C
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3.0
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No
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D
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3.1
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Yes
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E
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2.7
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Yes
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F
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2.6
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No
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G
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4.0
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No
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H
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3.8
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Yes
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I
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2.8
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Yes
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J
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3.6
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No
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