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.

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1. Introduction to Statistics53m

Intro to Stats
22m

Intro to Collecting Data
8m

Sampling Methods
23m

2. Describing Data with Tables and Graphs2h 1m

Visualizing Qualitative vs. Quantitative Data
4m

Frequency Distributions
35m

Histograms
7m

Histograms w/ Graphing Calculator
13m

Bar Graphs and Pareto Charts
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9m

Frequency Polygons
10m

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6m

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13m

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9m

3. Describing Data Numerically2h 8m

Mean
9m

Median
20m

Mode
7m

Standard Deviation
16m

Interpreting Standard Deviation
20m

Percentiles & Quartiles
14m

5-Number Summary Using a TI-84
10m

Boxplots
8m

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11m

Boxplots-Excel
8m

4. Probability2h 26m

Basic Concepts of Probability
7m

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6m

Addition Rule
17m

Multiplication Rule: Independent Events
11m

Introduction to Contingency Tables
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21m

Bayes' Theorem
13m

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8m

Counting
41m

5. Binomial Distribution & Discrete Random Variables3h 28m

Discrete Random Variables
38m

Binomial Distribution
1h 17m

Finding Binomial Probabilities-Excel
17m

Poisson Distribution
45m

Finding Poisson Probabilities-Excel
15m

Hypergeometric Distribution
14m

6. Normal Distribution & Continuous Random Variables2h 21m

Uniform Distribution
19m

Standard Normal Distribution
39m

Probabilities & Z-Scores w/ Graphing Calculator
19m

Non-Standard Normal Distribution
30m

Finding Probabilities, Z Values, and X Values with the Normal Distribution-Excel
32m

7. Sampling Distributions & Confidence Intervals: Mean3h 37m

Sampling Distribution of the Sample Mean and Central Limit Theorem
19m

Distribution of Sample Mean - Excel
23m

Introduction to Confidence Intervals
22m

Confidence Intervals for Population Mean
1h 26m

Determining the Minimum Sample Size Required
12m

Finding Probabilities and T Critical Values - Excel
28m

Confidence Intervals for Population Means - Excel
25m

8. Sampling Distributions & Confidence Intervals: Proportion1h 33m

Sampling Distribution of Sample Proportion
35m

Confidence Intervals for Population Proportion
45m

Confidence Intervals for Population Proportion - Excel
12m

9. Hypothesis Testing for One Sample3h 32m

Steps in Hypothesis Testing
1h 8m

Performing Hypothesis Tests: Means
46m

Hypothesis Testing: Means - Excel
42m

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28m

Hypothesis Testing: Proportions - Excel
27m

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Two Proportions
1h 12m

Two Proportions Hypothesis Test - Excel
28m

Two Means - Unknown, Unequal Variance
1h 2m

Two Means - Unknown Variances Hypothesis Test - Excel
12m

Two Means - Unknown, Equal Variance
15m

Two Means - Unknown, Equal Variances Hypothesis Test - Excel
9m

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12m

Two Means - Sigma Known Hypothesis Test - Excel
21m

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42m

Matched Pairs Hypothesis Test - Excel
12m

11. Correlation1h 24m

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26m

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21m

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6m

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17m

Inferences for the Correlation Coefficient - Excel
11m

12. Regression1h 59m

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26m

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12m

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12m

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32m

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13m

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23m

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50m

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18m

Goodness of Fit Test - Excel
10m

Contingency Tables
13m

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14m

Homogeneity Tests
11m

Using Matrices on a TI-84
6m

Independence Test Using TI-84
12m

Independence Tests - Excel
13m

14. ANOVA2h 1m

Introduction to ANOVA
34m

Multiple Comparisons: Tukey Test
14m

Multiple Comparisons: Tukey-Kramer Test
15m

Multiple Comparisons: Bonferoni Test
24m

Two-Way ANOVA
32m

7. Sampling Distributions & Confidence Intervals: Mean

Confidence Intervals for Population Mean

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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.

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Verified step by step guidance

Step 1: Understand the table structure. The table includes columns for Confidence Level (C), Significance Level (α), Area to the Left (α/2), Degrees of Freedom (df = n - 1), and Critical Value (tC = tα/2).

Step 2: Identify the given sample size (n = 30). Calculate the degrees of freedom using the formula df = n - 1. For n = 30, df = 30 - 1 = 29.

Step 3: For each confidence level (90%, 95%, 99%), determine the significance level (α). For example, α = 1 - Confidence Level. For 90%, α = 0.10; for 95%, α = 0.05; for 99%, α = 0.01.

Step 4: Divide the significance level (α) by 2 to find the Area to the Left (α/2). For example, for α = 0.10, α/2 = 0.05; for α = 0.05, α/2 = 0.025; for α = 0.01, α/2 = 0.005.

Step 5: Use a t-distribution table or calculator to find the critical value (tC = tα/2) corresponding to the calculated degrees of freedom (df = 29) and the Area to the Left (α/2) for each confidence level. Fill in the table with these values.