A manufacturer wants to increase the absorption capacity of a sponge. Based on past data, the average sponge could absorb 103.5ml. After the redesign, the absorption amounts of a sample of sponges were (in millilitres): 121.3, 109.2, 97.6, 103.5, 112.4, 115.3, 106.5, 112.4, 118.3, and 115.3. What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?
A) Do not reject null hypothesis if computed t is less than 2.580
B) Do not reject null hypothesis if computed t is less than 2.821
C) Reject null hypothesis if computed z is 1.96 or larger
D) Reject null hypothesis if computed t is less than 2.764

Question

Quizplus · Accepted Answer

The decision rule for a t-test at the 0.01 level of significance (two-tailed) for a small sample size (n<30) involves comparing the computed t-value to a critical t-value from the t-distribution table. Since the question implies a one-tailed test (increase in absorption), we look for the critical value at the 0.01 level for a one-tailed test. The correct critical value must be looked up based on the degrees of freedom (n-1) and the significance level. Choice B is correct because it specifies a critical value (2.821) that is plausible for a one-tailed test at the 0.01 level of significance for a sample of this size, although the exact critical value would depend on the degrees of freedom (which is 9 in this case). Other options either refer to a z-test, which is not appropriate for a small sample size, or specify incorrect critical values for a t-test at this level of significance.

A Manufacturer Wants to Increase the Absorption Capacity of a Sponge