An experiment is conducted to study the effects of curing times and curing temperatures on the bonding strength of an epoxy adhesive. In the experiment, two steel rods are adhered together End-to-end, and the bonding strength is defined as the force, in pounds, required to pull the bond Apart. For each combination of curing time and curing temperature, three tests are performed. The Results of the experiment are shown below. Can the main effect of curing temperature (low or high) on bonding strength be interpreted? If so, interpret the Main effect using the $\alpha = 0.05$ level of significance. A) Yes. Do not reject H₀. B) Yes. Reject H₀. C) No.

Question

Quizplus · Accepted Answer

To determine the main effect of curing temperature, we need to compare the mean bonding strengths at low and high temperatures, regardless of curing time. From the table, we see that the mean bonding strength is higher at high temperature (22.33) than at low temperature (18.33). To determine if this difference is statistically significant, we can perform a two-sample t-test with unequal variances, using the formula:

t = (x̄1 - x̄2) / sqrt(s1^2/n1 + s2^2/n2)

where x̄1 and x̄2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the values for low temperature and high temperature, we get:

t = (22.33 - 18.33) / sqrt((1.25^2/9) + (2.49^2/9)) = 2.56

Using a t-table with degrees of freedom = 4 (n1 + n2 - 2), we find the critical t-value for a two-tailed test with alpha = 0.05 to be 2.776.

Since our calculated t-value (2.56) is less than the critical t-value (2.776), we cannot reject the null hypothesis that there is no difference in bonding strength between low and high temperatures. Therefore, the main effect of curing temperature on bonding strength is not statistically significant at the 0.05 level of significance.

The correct answer is B.

An Experiment Is Conducted to Study the Effects of Curing α=0.05\alpha = 0.05α=0.05

An Experiment Is Conducted to Study the Effects of Curing $\alpha = 0.05$