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Find the critical value (or values) for the $t$ test for each.

a. $n=12, \alpha=0.01,$ left-tailed

b. $n=16, \alpha=0.05,$ right-tailed

c. $n=7, \alpha=0.10$, two-tailed

d. $n=11, \alpha=0.025,$ right-tailed

e. $n=10, \alpha=0.05,$ two-tailed

$a . -2.718$

$b .+1.753$

$c .\pm 1.943$

$d .+2.228$

$e,\pm 2.262$

Hypothesis Testing

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Lyka R.

May 12, 2021

Men spend an average of 29 minutes per day on weekends and holidays exercising and playing sports. They spend an average of 23 minutes per day reading. A random sample of 25 men resulted in a mean of 35 minutes exercising with a standard deviation of 6.9

Hi. This question. We're gonna see how to find that about you. So it doesn't explain something here. Then we're gonna go how to find the critical value from the table. So in both cases, for the left tail on, right till we gonna called one tailed, okay. And for the right tailed. Okay, it's gonna be the value from here, And it's always gonna be a positive value on for the left tail. That's gonna be the area from here, and it won't be a negative value. So whatever the value of here in the table, it's gonna be positive value. So we're gonna keep the sign for the right tail and for the love till we're gonna take that the same absolute value and put on negative a sign in front of it. And in case of to tail. Okay, you're gonna ah, get a positive value from the table. So the negative values gonna be here, this area on the positive ones gonna be from here, and I'm gonna show you in seconds How to find these Also on Microsoft Excel. So the 1st 1 is is asking about the Did you freedom 11 Because the sample size or end is 12 and Alfa is going on one. And, uh, it's asking about the left till so we get that 11 here. Okay, on degree of freedom, off point on one for one tail this one and this one's so you're gonna person you find it to a born 718 on the 2nd 1 is gonna be 1.753 Because in this 16 and the Alfa is buoyed on five and it's asking about the right tail. And the 3rd 1 is gonna be here because in this seven Alphas 70.1 and it is to tell. So it's gonna be one in the case, 1.9 43 and he minus one boy, nine for three on the 4th 1 is here because in this 11 So the degree of freedom is 10 and it's asking about point or 251 tail the right ones. It's gonna be positive. Value off 2.28 on the last one is about two tailed. So it's asking about Alphas 20.5 Andi in is 10 which is equivalently toe degree of freedom off nine. And it's gonna be also to values. The positive one is gonna be the upper one or 2.262 on that 111 is minus toe tothis too. And as you can see here, it's matching that that is that I compute from Microsoft Excel, and he is the function you are using. So if it is one tael, is you gonna It was he dot And then you just put that the C three, which is here, So and it will be Ah, and the probability all the Alfa okay. And then you gotta put the degree of freedom which happens here is will be in minus one. And if you are trying to compute, are just the right tail. So it's one till, but right one. You have to want a blood by minus one to get a buzz of value. But in case off having tea, which is to tell here you have toe to use dysfunctional just teed em. Just actually an abbreviation for inverse two tailed on following the same logic

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Hypothesis Testing