Find each probability. (B) P ( − 1.5 < T < 1.5 ) , d f = 8 P(-1.5<T<1.5),df=8

Welcome back. For this problem, I want to find the probability that negative 1.5 is less than t is less than 1.5, where my degrees of freedom is eight. Essentially, if I have my t distribution here, and we have negative 1.5 here and positive 1.5 here, I wanna find this area or this probability here. When I enter this type of problem into my TI 84, I'm going to need an upper and a lower bound for my t interval. So let's start with the lower bound. The smallest possible value that t could take would be anything slightly, slightly bigger than negative 1.5. So my lower bound is going to be negative 1.5. My upper bound similarly is going to be 1.5, which is really the upper limit of what my t score could be. So my upper bound is going to be positive 1.5. I'll also need my degrees of freedom, which we have here. Now that I have all the information, let's use our t I 80 fours. I'm gonna start by clicking on the second and then variables button to go to the distribution menu. I need the TCDF function, which is option six, so I'll click six. And that's step one, all set. You'll notice that the previous information from part a might already be in your calculator. I can just type over it. In this case, my lower bound is negative 1.5. My upper bound is positive 1.5, and my degrees of freedom is still eight. Once I have that all set, that's step two done. Now I just need to click on enter when I'm over paste, and I'll see it appear in my viewing window. I'll click enter one more time for my calculator to find that probability. That's step three, all set. And I'll notice that the probability is approximately 0.83. So I have about an 83% chance of my t score falling between negative 1.5 and positive 1.5. Great work.

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7. Sampling Distributions & Confidence Intervals: Mean

Confidence Intervals for Population Mean

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Multiple Choice

Find each probability.
(B) $P (- 1.5 < T < 1.5), d f = 8$

0.91

0.83

0.083

0.086

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Verified step by step guidance

Step 1: Understand the problem. The goal is to find the probability that the t-statistic (T) falls between -1.5 and 1.5, given that the degrees of freedom (df) are 8. This involves using the t-distribution table or a statistical software/calculator.

Step 2: Recall that the t-distribution is symmetric and centered at 0. The probability of a range can be calculated by finding the cumulative probability up to 1.5 and subtracting the cumulative probability up to -1.5.

Step 3: Use the t-distribution table or software to find the cumulative probability for T = 1.5 with df = 8. This value represents the area under the curve to the left of 1.5.

Step 4: Similarly, find the cumulative probability for T = -1.5 with df = 8. Since the t-distribution is symmetric, this value can be calculated as 1 minus the cumulative probability for T = 1.5.

Step 5: Subtract the cumulative probability for T = -1.5 from the cumulative probability for T = 1.5 to find the probability that T falls between -1.5 and 1.5. This is the final result.