Question

A finance magazine states u.s. families have 15,000 dollars of debt, on average. Karen, a financial planner, would like to test the claim that the average amount of debt owed by U.S. families is lower than the generally accepted time of 15,000 dollars. To test this claim, at the 10

Answer 1

To test the claim that the average amount of debt owed by U.S. families is lower than $15,000, Karen would need to conduct a hypothesis test. The steps for conducting a hypothesis test include stating the hypotheses, setting the significance level, collecting and analyzing data, calculating the test statistic, determining the critical region, making a decision, and interpreting the results.

Step-by-step explanation:

The subject of this question is Mathematics, specifically statistical hypothesis testing.

To test the claim that the average amount of debt owed by U.S. families is lower than the generally accepted time of $15,000, Karen would need to conduct a hypothesis test.

Here are the steps for conducting a hypothesis test:

1. State the hypotheses: The null hypothesis (H0) assumes no difference or no effect, so in this case, the null hypothesis is that the average amount of debt owed by U.S. families is $15,000. The alternative hypothesis (Ha) assumes there is a difference or effect, so in this case, the alternative hypothesis is that the average amount of debt owed by U.S. families is lower than $15,000.
2. Set the significance level (alpha): This is the probability of rejecting the null hypothesis when it is true. Commonly used significance levels are 0.05 or 0.01.
3. Collect and analyze the data: Karen would need to collect data on the debt amounts owed by a sample of U.S. families. She can then calculate the sample mean and sample standard deviation.
4. Calculate the test statistic: The test statistic depends on the type of test being conducted. In this case, since she wants to test if the average amount of debt is lower, she would use a one-sample t-test. She can calculate the test statistic using the formula: t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size)).
5. Determine the critical region: The critical region is the range of test statistic values that would lead to rejection of the null hypothesis. For a one-tailed test, where the alternative hypothesis is that the average amount of debt is lower, Karen would compare her test statistic to the critical value from the t-distribution table.
6. Make a decision: If the test statistic falls within the critical region, Karen would reject the null hypothesis in favor of the alternative hypothesis. If the test statistic does not fall within the critical region, Karen would fail to reject the null hypothesis.
7. Interpret the results: If Karen rejects the null hypothesis, she would conclude that there is evidence to support the claim that the average amount of debt owed by U.S. families is lower than $15,000. If she fails to reject the null hypothesis, she would not have sufficient evidence to support the claim.