# Construct a 95% confidence interva

label Statistics
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A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following GPAs.

 College A College B 3.7 3.8 2.8 3.2 3.2 4.0 3.0 3.0 3.6 2.5 3.9 2.6 2.7 3.8 4.0 3.6 2.5 3.6 2.8 3.9 3.4

Construct a 95% confidence interval for the difference between the mean GPA of college A students and the mean GPA of college B students.

Jul 29th, 2015

To calculate a confidence interval for the population mean (average), under these conditions, do the following: Determine the confidence level and degrees of freedom and then find the appropriate t*-value. Find the sample mean. Multiply t* times s and divide that by the square root of n

You estimate the population mean,

by using a sample mean,

plus or minus a margin of error. The result is called a confidence interval for the population mean,

In many situations, you don’t know

so you estimate it with the sample standard deviation, s; and/or the sample size is small (less than 30), and you can’t be sure your data came from a normal distribution. (In the latter case, the Central Limit Theorem can’t be used.) In either situation, you can’t use a z*-value from the standard normal (Z-) distribution as your critical value anymore; you have to use a larger critical value than that, because of not knowing what

is and/or having less data.

The formula for a confidence interval for one population mean in this case

is the critical t*-value from the t-distribution with n – 1 degrees of freedom (where n is the sample size).

Jul 29th, 2015

 -0.81 < μ1 - μ2 < 0.15

Jul 29th, 2015

exactly that, you must have used the formula correctlt

Jul 29th, 2015

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Jul 29th, 2015
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Jul 29th, 2015
Nov 21st, 2017
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