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I am doing an assignment for class and I have hit a wall. I'm not sure what to do next.

Using a sample with 12 discrete elements, I am trying to test a hypothesis that the population mean is 243 with significance level .05.

Here is what I have so far (this has been verified):

n = 12 x bar = 244.33 s = 12.382

t = (244.33 - 243) / (12.382 / sqrt(12)) = .3720

The next step should be to calculate the P-value, which I do by looking up .3720 on the t-table with df = n-1 = 11, however there are no values on the t-table less than 1. Therefore I don't know how to look up .3720.

I feel like there is some crucial bit of knowledge I'm missing that is stopping me from completing this problem.

I would really appreciate some assistance in knowing how to calculate the P-value from here.

Thank you very much.

UPDATE: I appreciate everyone's comments but I feel as though I'm getting a lot of complicated answers. This is a question out of my textbook and isn't supposed to require any special software or anything like that, just a simple calculator and a t-table.

Maybe it would be easier to ask the question from the text ad verbatim:

*A random sample of n = 12 frozen dinners of a certain type was selected from production during a particular period, and the calorie content of each one was determined. Here are the resulting observations. The stated calorie content is 243. Carry out a formal test of the hypothesis that the population mean = 243, with a significance level of .05. Observations:
255 244 239 242 265 245 259 248 225 226 251 233 *

Scortchi - Reinstate Monica
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user2779949
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    There are online calculators for getting p from t. – Peter Flom Apr 07 '14 at 23:10
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    One approach is to find the smallest t-value your table contains (at the right d.f) and say that the p-value is larger than that; this would probably be sufficient. However, tables come in many different formats and it would be best if you indicated how the table is organized. Another approach would be to compute an approximate p-value from a numerical integration of the density (Simpson's rule on the 3 points (0,t/2,t) gives better than 4 figure accuracy on your problem). A third approach would be to use a statistical package or online calculator. – Glen_b Apr 08 '14 at 00:10
  • There's also the possibility that you may prefer to use some form of [interpolation](http://stats.stackexchange.com/questions/64538/how-do-i-find-values-not-given-in-interpolate-in-statistical-tables) in the table (given we know the one-tailed p-value for t=0). – Glen_b Apr 08 '14 at 00:26
  • Note you're not being asked for an exact p-value. – Scortchi - Reinstate Monica Apr 08 '14 at 11:38
  • I have seen people report t<1 and F<1 without p values in the past, because this information is arguably redundant. – Behacad Apr 08 '14 at 12:24
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    You have all the information you need, because the t distribution is almost linear in the missing part of the table. Your table gives you values close to $1$, say at $1+\epsilon$. You know the distribution is symmetric around $0$, so its value at $0$ must be $1/2$. Using these known values at $0, 1,$ and $1+\epsilon$ you can *interpolate*. The interpolation function will be approximately $0.5+0.38 t-0.05 t^3$. This is accurate to within $\pm 0.003$ in the range $-1\le t\le 1$ and that's more than accurate for almost any purpose. *E.g.*, when $t=0.372$ it gives $0.639$ instead of $0.642$. – whuber Apr 08 '14 at 19:55

1 Answers1

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You are not going to reject your null hypothesis if the absolute value of your test statistic is less than $1$.

If you must have a p-value, you could use statistical software. For example R gives

> pt(q=abs(0.3720), df=11, lower.tail = FALSE)
[1] 0.3584799
> 
> 2*pt(q=abs(0.3720), df=11, lower.tail = FALSE)
[1] 0.7169597

and you probably want the second if you are applying a two-sided test.

Henry
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