How much more do public colleges and universities charge...

How much more do public colleges and universities charge out-of-state students for tuition per year? A random sample of 19 public colleges and universities listed at www.collegeboard.com yielded the following data for students entering as Freshmen in Fall $2013 .$ a) Create a $90 \%$ confidence interval for the mean difference in cost. Be sure to justify your procedure. b) Interpret your interval in context. c) A national magazine claims that public institutions charge state residents an average of $\$ 7000$ less than out-of-staters for tuition each year. What does your confidence interval indicate about this assertion?

How much more do public colleges and universities charge out-of-state students for tuition per year? A random sample of 19 public colleges and universities listed at www.collegeboard.com yielded the following data for students entering as Freshmen in Fall $2013 .$ a) Create a $90 \%$ confidence interval for the mean difference in cost. Be sure to justify your procedure.
b) Interpret your interval in context.
c) A national magazine claims that public institutions charge state residents an average of $\$ 7000$ less than out-of-staters for tuition each year. What does your confidence interval indicate about this assertion?

Key Concepts

Confidence Interval

A confidence interval is a range of values, derived from the sample data, that is likely to cover the true population parameter with a specified degree of confidence (such as 90%). It provides a way to infer the value of a population parameter and assess the uncertainty around the estimate.

t-Distribution

The t-distribution is used when the sample size is small and the population standard deviation is unknown. It accounts for the extra uncertainty due to estimating the standard deviation from a small sample, making it particularly important in constructing confidence intervals and conducting hypothesis tests in such scenarios.

Paired Sample Analysis

Paired sample analysis involves comparing two related scores or measurements for each subject or match-pair. This approach reduces variability by accounting for the condition that the differences within pairs are more homogeneous than those taken from independent samples, thereby providing a more powerful test for differences between paired observations.

Hypothesis Testing with Confidence Intervals

This concept involves using the confidence interval to evaluate a claim about a population parameter. In practice, if a hypothesized value does not fall within the calculated confidence interval, it provides evidence to reject the hypothesis at the specified confidence level. Conversely, if it falls within the interval, the data do not provide strong evidence against the claim.

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