a) What is the critical value for this analysis? Round answers to 4 decimal places.

Critical value: [tex]t = \text{___}[/tex]

b) Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions.

Select from the drop-down menu to shade to the left, to the right, between, or left and right of the [tex]z[/tex]-score(s).

(Note: the arrows can only be dragged to match the horizontal axis tick marks, so just position the shaded boundary to be as close to your critical value as possible).

Shade: [Select an option from the drop-down menu]

Click and drag the arrows to adjust the values.

A set of 16 unalloyed steel specimens were cut in half, one half being sent for analysis to a laboratory in Europe and the other half being sent to a laboratory in Asia. Engineers want to test the claim that the European lab results were different from the Asian lab results at a significance level of [tex]\alpha = 0.05[/tex].

For the context of this problem, [tex]H_a: \mu_{\text{Europe}} - \mu_{\text{Asia}} \neq 0[/tex], where the first data set represents the test results from the European lab, and the second data set represents the test scores from the Asian lab. Assume the population is normally distributed.

[tex]H_0: \mu_{\text{Europe}} - \mu_{\text{Asia}} = 0[/tex]
[tex]H_a: \mu_{\text{Europe}} - \mu_{\text{Asia}} \neq 0[/tex]

The engineers receive the following data from the two laboratories:

Europe: 44.5, 45.6, 27.1, 16.1, 19.1, 64, 48.9, 27.5, 66.9, 75.3, 28.6, 26.7, 79.6, 50.5, 57.4, 39.1
Asia: 36.3, 40, 35.8, 27, 43.8, 42.2, 60.6, 35.5, 49, 52.3, 37.3, 36.1, 36.3, 50.3, 35, 40.4

c) What is the test statistic for this sample? Round answers to 4 decimal places.

Test Statistic: [tex]t = \text{___}[/tex]

This test statistic leads to a decision to... [Select an answer from the drop-down menu]

As such, the final conclusion is that... [Select an answer from the drop-down menu]