Question

Consider the following output for a one-sample procedure from R's t.test. One Sample t-test data: data t = 4.1894, df = 49, p-value = 0.0001162 alternative hypothesis: true mean is not equal to 15 95 percent confidence interval: 16.61141 19.58255 sample estimates: mean of x 18.09698 Which of the following statements are true? There may be more than one correct statement; check all that are true. a) We can be 95% confident that the sample mean lies between 16.61141 and 19.58255

Answer 1

The given output is from R's t.test, representing a one-sample t-test. The p-value is less than 0.05, so we reject the null hypothesis and conclude that there is evidence of a significant difference between the sample mean and the population mean. The 95 percent confidence interval provides a range within which we can have at least a 95% confidence that the true population mean lies.

Step-by-step explanation:

The given output is from R's t.test, representing a one-sample t-test. The null hypothesis states that the true mean is equal to 15, and the alternative hypothesis states that the true mean is not equal to 15. The output gives the t-value, degrees of freedom, and the p-value. In this case, the p-value is 0.0001162, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that there is evidence of a significant difference between the sample mean and the population mean.

The 95 percent confidence interval provided (16.61141 to 19.58255) does not play a role in making the decision of rejecting or not rejecting the null hypothesis. However, the correct statement is that there is at least a 95% confidence that the true population mean lies within this interval.