Question

Basic concepts. For each of the following answer the question and give a short explanation of your reasoning. a) A 95% confidence interval for the difference between two means is reported as (0.8, 2.3). What can you conclude about the results of a significance test of the null hypothesis that the population means are equal versus the two-sided alternative? b) Will larger samples generally give a larger or smaller margin of error for the difference between two sample means? c) A significant test for comparing two means gave t = −1.97 with 10 df. At the 5% significance level, can you reject the null hypothesis that the population mean are equal versus the two-sided alternative? d) Answer part c) for the one-sided alternative that the difference between the population mean is negative.

Answer 1

a) Since the interval does not contain 0, so we should reject the null hypothesis.

b) The larger samples will give smaller margin of error for the difference between two sample means.

Because, as the sample size increases, the standard of error decreases, So that the margin of error also decreases.

c) At alpha = 0.05, the critical values are +/- t_0.025,10 = +/- 2.228

Since the test statistic value is not less than the lower critical value(-1.97 > -2.228), so we should not reject the null hypothesis.

d) At alpha = 0.05, the critical value is t_{0.05, 10} = -1.812

Since the test statistic value is less than the critical value(-1.97 < -1.812), so we should reject the null hypothesis.