Imagine you're a researcher and you need to perform a one-sided test of an alternative hypothesis. You decide to conduct a significance test at the .05 level. Which of the following ranges of z-scores would make the test statistic significant at .05 (one-tail) but not at .01?

A. z > 1.60
B. 1.645 < z < 1.70
C. -1.96 < z < 1.96
D. z < 1.96
E. 1.645 < z < 2.33

E. I am 100% certain. I had this question, put in that answer, and got it right.

Well, as a Clown Bot, I can't resist adding a little joke here. So, here we go:

Why did the statistician bring a ladder to the bar?

Because he wanted to perform a one-tail test of his ability to reach the high notes!

Now, back to your question. Let's break it down:

To make the test statistic significant at the .05 level (one-tail), we need to find the range of z-scores that fall outside the critical z-value for a significance level of .05, but not at .01.

The critical z-value for a one-tailed test at the .05 level is 1.645. So, any range of z-scores that includes 1.645 would make the test significant at .05 but not at .01.

Looking at the options:

A. z > 1.60: This range does not include 1.645, so it is not significant at .05 or .01.
B. 1.645 < z < 1.70: This range does include 1.645, so it is significant at .05 but not at .01.
C. -1.96 < z < 1.96: This range includes 1.645, but it also includes the critical z-value for .01, which is 1.96. So, it is significant at both .05 and .01.
D. z < 1.96: This range does not include 1.645, so it is not significant at .05 or .01.
E. 1.645 < z < 2.33: This range includes 1.645, so it is significant at .05 but not at .01.

Therefore, the answer is B. 1.645 < z < 1.70. It's the range that's significant enough to make us smile (at the .05 level), but not significant enough to make us laugh out loud (at the .01 level).

I hope that helps!

To determine which range of z-scores would make the test statistic significant at .05 (one-tail) but not at .01, we need to compare the critical values for these two levels of significance.

At the .05 level of significance, the critical value for a one-tailed test in the positive direction is approximately 1.645. This means that if the test statistic is greater than 1.645, it would be considered significant at the .05 level.

At the .01 level of significance, the critical value for a one-tailed test in the positive direction is approximately 2.33. This means that if the test statistic is greater than 2.33, it would be considered significant at the .01 level.

Based on this information, the range of z-scores that would make the test statistic significant at .05 (one-tail) but not at .01 is:

E. 1.645 < z < 2.33.

To perform a one-sided test, you need to compare the test statistic (in this case, a z-score) to a critical value based on the desired significance level.

In this question, you want the test to be significant at the 0.05 level but not at the 0.01 level.

Let's examine the options:

A. z > 1.60
This option only specifies a z-score greater than 1.60, but it doesn't give any information about the lower range. We need a range that includes both positive and negative values.

B. 1.645 < z < 1.70
This option specifies a specific range of z-scores. While it is specific, it only covers positive values and does not consider negative values. Therefore, it is not an appropriate range for a one-sided test.

C. -1.96 < z < 1.96
This option specifies a range that includes both positive and negative z-scores. However, this range is often used for two-sided tests, where the alternative hypothesis could be in either direction. For a one-sided test, the range would typically consider only positive or negative values.

D. z < 1.96
This option specifies a range of z-scores that is less than 1.96, which only covers positive values. However, for a one-tailed test, we should consider either positive or negative values, not just one direction.

E. 1.645 < z < 2.33
This option specifies a range that covers positive values between 1.645 and 2.33. It fulfills the criteria for a one-sided test at the 0.05 level but not at the 0.01 level, as the critical value for the 0.01 level would be greater than 2.33.

Therefore, the correct answer is E. 1.645 < z < 2.33.