Questions: A recent article claims that the state of Illinois has low tuition rates for its colleges and universities. Cate decides to research the cost of tuition for different colleges in Illinois. The average tuition in Illinois is 28,950 with a standard deviation of 3,470. Which type of inference test should Cate use? a) One-sample t-test b) Two-way ANOVA c) One-sample z-test d) Chi-squared test for goodness of fit

Solution Steps

To determine which type of inference test Cate should use, we need to consider the nature of the data and the hypothesis being tested. Cate is interested in comparing the average tuition cost to a known population mean. Given that the population standard deviation is known, the appropriate test is a one-sample z-test.

Cate wants to determine if the average tuition in Illinois is significantly different from a known value. The problem provides the average tuition and standard deviation for colleges in Illinois.

To determine the appropriate inference test, we need to consider the following:

• We have a single sample (tuition rates in Illinois).
• We are comparing the sample mean to a known population mean.
• The population standard deviation is known.

Given the conditions:

• One-sample t-test is used when the population standard deviation is unknown.
• Two-way ANOVA is used for comparing means across multiple groups and factors.
• One-sample z-test is used when the population standard deviation is known.
• Chi-squared test for goodness of fit is used for categorical data to see if observed frequencies match expected frequencies.

Since the population standard deviation is known, the appropriate test is the one-sample z-test.

Final Answer