Consider a paired t-test. The setting is that two normal random variables (X) and (Y) are sampled. We pair each of the samples from the first variable with each of the samples from the second variable, and we check the "null hypothesis" that the two elements in each pair have the same mean, i. e. μX=μY, against the alternative hypothesis that μX≠μY. Now create a new random variable (D) by taking the difference between the two elements in each pair. The Null Hypothesis is defined as μD=0, and the alternative hypothesis μD≠0. Note that if the two variables are normally distributed, their difference (D) is also normally distributed. We then calculate the confidence interval for the mean of D .

Select an option: yes, no, or can't tell, for each question:

1) Suppose that for a given data set of D, a 95% confidence interval is calculated to be (-3.45,1.78). If you were to perform a hypothesis test at the 5% significance level to test the null hypothesis, would you reject it?

2) Suppose that for a given data set of D, a 99% confidence interval is calculated to be (-10.77,-2.35). If you were to perform a hypothesis test at the 1% significance level to test the null hypothesis, would you reject it?

3) Suppose that for a given data set of D, a 97% confidence interval is calculated to be (25.6,41.1). If you were to perform a hypothesis test at the 3% significance level to test the null hypothesis, would you reject it?