Questions 6–10 refer to the sample data in the following table, which describes the fate of the passengers and crew aboard the Titanic when it sank on April 15, 1912. Assume that the data are a sample from a large population and we want to use a 0.05 significance level to test the claim that surviving is independent of whether the person is a man, woman, boy, or girl.

Is the hypothesis test left-tailed, right-tailed, or two-tailed?

검증된 단계별 안내

Step 1: Understand the hypothesis test. The claim is that surviving is independent of whether the person is a man, woman, boy, or girl. This means we are testing for independence between two categorical variables: survival status (survived or died) and gender/age group (men, women, boys, girls).

Step 2: Determine the type of test. Since we are testing for independence between two categorical variables, a Chi-Square Test for Independence is appropriate.

Step 3: Identify the significance level. The problem specifies a significance level of 0.05, which will be used to compare the p-value obtained from the test.

Step 4: Decide the tail of the test. A Chi-Square Test for Independence is inherently a two-tailed test because it evaluates whether there is any association (positive or negative) between the variables, not just one direction.

Step 5: Prepare the contingency table. The table provided in the image already serves as the contingency table, showing the observed frequencies for each combination of survival status and gender/age group. These values will be used to calculate the expected frequencies and the Chi-Square statistic.

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주요 개념

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Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample data to determine whether to reject H0. In this context, the null hypothesis would state that survival is independent of gender, while the alternative would suggest a dependence.

Significance Level

The significance level, denoted as alpha (α), is the threshold for determining whether to reject the null hypothesis. A common significance level is 0.05, which indicates a 5% risk of concluding that a difference exists when there is none. In this case, it means that if the p-value is less than 0.05, we would reject the null hypothesis regarding survival independence.

Types of Hypothesis Tests

Hypothesis tests can be classified as left-tailed, right-tailed, or two-tailed based on the nature of the alternative hypothesis. A left-tailed test checks for a decrease in a parameter, a right-tailed test checks for an increase, and a two-tailed test checks for any difference. In this scenario, since we are testing for independence without a specific direction, it would typically be a two-tailed test.