Find the critical val. ( t α ⁄ 2 ) (t_{\alpha⁄2}) for each confidence interval. (B) Confidence Level = 90 % , n = 48 90\%,n=48

Welcome back. For this problem, we wanna find the critical value t sub alpha over two for each confidence interval. This time, we have a confidence level of 90% and an n value of 48. As a reminder, to enter this information into our t I 84, I'm going to need my alpha over two value and my degrees of freedom. To find alpha over two, I am going to need my significance level alpha. My significance level is going to be one minus my confidence level, so it's going to be one minus point nine or point one. That means that my alpha over two is going to be point one divided by two, which is 0.05. My degrees of freedom is n minus one. My n value is 48, so my degrees of freedom will be 47. Once I have that information all set, I'm ready to take out my t I 84 and find my t critical value. As a reminder, the calculator will give me negative t sub alpha over two, and I'll just remove the negative sign to get t sub alpha over two, my positive critical value. Alright. So the first step is to click on second and then variables to go to the distribution menu, and then click on four to take me to the t inverse function. That's step one. All set. For step two, I need to enter in my area to the left, which is my alpha over two or 0.05 and my degrees of freedom, which in this case is 47. Once that's all set, that's step two done, and I can scroll down to paste, click enter, and see it appear in my viewing window. I'll click enter one more time to get my calculator to evaluate it, and I end up getting approximately negative 1.68 as the negative critical value. So the positive one will be 1.68. That's gonna be t sub alpha over two. Great work.

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- Sampling Distribution of Sample Proportion
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- Confidence Intervals for Population Proportion
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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. $open paren t sub alpha fraction slash 2 close paren$ for each confidence interval.
(B) Confidence Level = $90 percent sign comma n equals 48$

2.41

2.68

1.68

1.30

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Verified step by step guidance

Step 1: Understand the problem. You are tasked with finding the critical value (t_{α⁄2}) for a given confidence level and sample size. The confidence level is 90%, and the sample size (n) is 48.

Step 2: Determine the degrees of freedom (df). The degrees of freedom for a t-distribution is calculated as df = n - 1, where n is the sample size. For this problem, df = 48 - 1.

Step 3: Identify the significance level (α). The significance level is calculated as α = 1 - (confidence level). For a 90% confidence level, α = 1 - 0.90 = 0.10.

Step 4: Divide the significance level by 2 to find α⁄2. This is because the t-distribution is symmetric, and the critical value corresponds to the area in the two tails. α⁄2 = 0.10 / 2.

Step 5: Use a t-distribution table or statistical software to find the critical value (t_{α⁄2}) corresponding to α⁄2 and the degrees of freedom (df). Locate the row for df = 47 and the column for α⁄2 = 0.05 to find the critical value.