Find the critical val. ( t α / 2 ) (t_{\alpha/2}) for each confidence interval. (A) Confidence Level = 95 % , n = 35 95\%,n=35

Welcome back. For this problem, we wanna find the t critical value for each confidence interval, and we're starting with a confidence level of 95% and an n value of 35. So as a reminder, to enter in the information on our TI 80 fours, we're going to need a couple pieces of information. We'll need alpha over two, and we will need our degrees of freedom. Now to find alpha over two, I wanna actually start by finding alpha. My alpha value is going to be one minus my confidence level, which is point nine five. So my alpha is going to be point zero five, and my alpha over two is going to be point zero five divided by two, which is point zero two five. My degrees of freedom is n minus one, so that's going to be 35, my n value minus one, which is 34. Now that I have this information, I'm ready to use my t I 84 to find my t critical value. As a reminder, the t I 84 will tell me my negative t sub alpha over two, and I wanna find my t sub alpha over two. So I'll take my calculator value, and I'll end up removing that negative sign. Alright. Let's follow the steps and dive right in. I'm going to start by clicking on the second then variables button to take me to the distribution menu. I want option four, so I'll click on the four button. That's step one. All set. For step two, I just need to enter in some information starting with alpha over two, which is 0.025, and my degrees of freedom, which is 34. Once that's all set, I'll scroll down to paste and click enter. That's step two, all set. And I click enter one more time to have my calculator evaluate my t critical value. That's step three. All set. I can see that the value is approximately negative 2.03, so that means that my t sub alpha over two is going to be positive 2.03. Awesome work.

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1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
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- Sampling Distribution of Sample Proportion
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- Confidence Intervals for Population Proportion
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14. ANOVA1h 0m

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

Find the critical val. $open paren t sub alpha divided by 2 close paren$ for each confidence interval.
(A) Confidence Level = $95 percent sign comma n equals 35$

2.73

2.44

1.69

2.03

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Verified step by step guidance

Step 1: Understand the problem. We are tasked with finding the critical value (t_{α/2}) for a given confidence level and sample size. The confidence level is 95%, and the sample size (n) is 35.

Step 2: Recall the formula for degrees of freedom (df) in a t-distribution. Degrees of freedom are calculated as df = n - 1, where n is the sample size. For this problem, df = 35 - 1.

Step 3: Identify the significance level (α). For a 95% confidence level, the significance level is α = 1 - 0.95 = 0.05. Since we are looking for t_{α/2}, divide α by 2 to get α/2 = 0.05 / 2.

Step 4: Use a t-distribution table or statistical software to find the critical value t_{α/2} corresponding to df = 34 (calculated in Step 2) and α/2 = 0.025 (calculated in Step 3).

Step 5: Verify the critical value from the options provided. The correct critical value should match the one obtained from the t-distribution table or software.