Consider a random sample of 11 observations, given in the following, from a normal population with hypothesized mean 57.71.
59.94 58.93 59.41 60.66 59.00 60.98 58.85 55.21 59.02 61.14 59.25
Compute the value of the test statistic for H0 : µ = 57.71 versus Ha : µ > 57.71 with α = 0.01. Draw a conclusion about the population mean.
Write down the formula to get the p value associated with this hypothesis test
- For the first part, I found the SD and it came out to be around 1.603650835
Based on the SD, I found the "t". t = 0.997723422
Now To find the P-Value, i need to know the DF but I am not to sure what the DF would be.
So I am assuming that DF is the Sample Size (11 in this case - 1 = 10). A lot of resources said to use Minitab or R to find the P value but I am not allowed to use any of that. I am pretty sure that there is a manual way to find out the P value. So can someone help me find the P-Value or the steps I have to take to get to the P-Value.
You should say that you calculated the mean to be about $\bar{x}=59.30818$ as well as your sample standard deviation of $s=1.603650835$
You have miscalculated $t$: it should then be $\sqrt{n}\left( \dfrac{\bar{x}-57.71}{s}\right)$ which is about $3.3$ here. Your calculation was a factor of $\sqrt{11}$ too small; perhaps you forgot that the standard error of the mean is smaller than the standard deviation of the distribution
I have some doubts whether you are going to be able to find a $p$-value without tables or a computer