Fill out the table using a calculator and n = 30 n=30 .

Welcome to the practice. For this problem, we want to fill in the table, so we want to find some critical values using our confidence levels and n is 30. Why don't we dive right in starting with c equaling 90%. If our confidence level is 90%, that means that our significance level is one minus that or point one. So our area to the left, which is alpha over two, is going to be 0.1 divided by two, which is 0.05. Lastly, we need our degrees of freedom, which is n minus one. So in this case, that will be 30 minus one, which is 29. Now we're ready to use our t I 80 fours. We're gonna start by clicking on second, then variables to get to the distribution menu, and then clicking on option four. That's step one. All set. For step two, we just wanna enter in some information starting with alpha over two, which is 0.05, and our degrees of freedom, which is 29. Once that's all set, that's step two done. Then we'll scroll down to paste and click enter. It's in our viewing window here, so we'll click enter one more time to get that t critical value. As a reminder, the calculator gives us the negative version. We want the positive version here, so I'm just gonna remove the negative sign. It's approximately 1.7 as that t critical value. And we are all set with our steps. Now we just wanna do the same thing for the remaining two confidence levels. So let's now go to a 95% confidence level. That means that our significance level is 0.05, and our area to the left is going to be 0.05 or alpha divided by two, which is 0.025. Our degrees of freedom is still gonna be 30 minus one, which is 29. And now we're ready to use the same process on our calculator to find our critical value. I'm gonna click on second, then variables, and go to option four. That's step one all set. You'll notice that the previous information is still in the menu. I need to change my area to the left to my new alpha over two, which is 0.025, but my degrees of freedom is still 29. So that's step two, all set. And I'm just going to go to paste and click enter, then click enter one more time to actually get that value. Again, it gives me the negative value and I just want the positive one, so I'll remove that negative sign. It ends up being approximately 2.05. We have one more confidence level left, 99%. And that means that our significance level is going to be 0.01, That's our alpha, and alpha over two is 0.01 divided by two, which is 0.005. Our degrees of freedom is still 30 minus one, which is 29. And now we just go through the steps one more time. I'll click on the second, then variables button to go to the distribution menu, and option four. That's step one. All set. Now I just need to change the information to match my current information. So my new alpha over two is 0.005. My degrees of freedom is still 29, so I'll scroll down to paste and click enter. That's step two. All set. Clicking enter one more time will get me that value. So that's step three. All set. As a reminder, this is the negative version, so I just remove the negative sign to get the positive version, which is 2.76, my t critical value. Awesome work.

7. Sampling Distributions & Confidence Intervals: Mean

Confidence Intervals for Population Mean

Statistics

7. Sampling Distributions & Confidence Intervals: Mean

Confidence Intervals for Population Mean

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Multiple Choice

Fill out the table using a calculator and $n equals 30$ .

Table displaying confidence levels, significance levels, area to the left, degrees of freedom, and critical values for statistical analysis.

Table displaying confidence levels, significance levels, areas to the left, degrees of freedom, and critical values for statistical analysis.

Table displaying confidence levels, significance levels, areas to the left, degrees of freedom, and critical values for population mean.

Table displaying confidence levels, significance levels, area to the left, degrees of freedom, and critical values for statistical analysis.

Verified step by step guidance

Identify the given values in the problem: the sample size (n = 30), the confidence levels (90%, 95%, 99%), and the corresponding significance levels (α = 0.10, 0.05, 0.01).

Calculate the degrees of freedom (df) using the formula df = n - 1. Since n = 30, df = 30 - 1 = 29.

Determine the area to the left of the critical value for each confidence level. This is calculated as α/2. For example, for a 90% confidence level, α = 0.10, so α/2 = 0.05.

Using a t-distribution table or calculator, find the critical t-value (t_c) for each confidence level based on the calculated degrees of freedom (df = 29) and the area to the left (α/2).

Fill in the table with the calculated values for the area to the left, degrees of freedom, and critical t-values for each confidence level.