Question

random samples of 1546 men and 1678 women have been given a scale that measures support of legal abortion. men average 12.45 and women average 12.46, and the difference is significant at the 0.05 level. what can we conclude?

Answer 1

To test for a significant difference in support of legal abortion between men and women, a two-sample t-test can be conducted using the given sample data. If the test statistic is greater than the critical value at a 0.05 significance level, there is a significant difference in support of legal abortion between men and women.

Step-by-step explanation:

To determine if there is a significant difference in support of legal abortion between men and women, we can conduct a hypothesis test using the given sample data.

1. Null hypothesis (H0): The population means of support of legal abortion for men and women are equal.
2. Alternative hypothesis (H1): The population means of support of legal abortion for men and women are different.
3. We can use a two-sample t-test to compare the means of the two independent samples. With the given sample sizes, we can assume that the sampling distribution of the means is approximately normal based on the Central Limit Theorem.
4. Calculate the test statistic using the formula: t = (mean1 - mean2) / sqrt((s1^2 / n1) + (s2^2 / n2)), where mean1 and mean2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
5. Using the test statistic, degrees of freedom, and the chosen significance level of 0.05, we can find the critical value from the t-distribution table or use statistical software.
6. If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a significant difference in support of legal abortion between men and women. If not, we fail to reject the null hypothesis.