Question 1076812
Calculating the t test statistic


t = (xbar - mu)/(s/sqrt(n))
t = (4.40-4.66)/(0.28/sqrt(6))
t = -2.27452618972722
t = -2.275


The t test statistic is approximately -2.275


----------------------------------------------------------------------------------

Calculating the p value


We have two basic options to calculate the p value: a) using a table or b) using a calculator


Since your teacher wants it accurate to 4 decimal places, we'll have to use a calculator to get the desired accuracy. Using a TI calculator, you would type in  <font color=blue>tcdf(-99,-2.275,5)</font> as shown below
<img src = "http://image.prntscr.com/image/c03aa971318742a99e84efd1b13ee79d.png">
Note: Hit the 2ND key up at the top corner, then hit the VARS key. Scroll down to "tcdf" which is option number 6. The first two numbers "-99, -2.275" are the left and right bounds of the interval. Effectively this is the same as saying "everything to the left of -2.275. The last value 5 is the degrees of freedom (df = n-1 = 6-1 = 5)


Doing all that, we get the p value of roughly 0.0359934669 which rounds to 0.0360 when you round to four decimal places. 


Side Note: if you don't have a TI calculator, then you can use online calculators, such as <a href = "http://stattrek.com/online-calculator/t-distribution.aspx">this one</a>, to calculate the p value.