Interpretation of a Q-Q plot and Shapiro-Wilk test

#1
I have the following output from a shapiro-wilk test:

Shapiro-Wilk normality test data: goalTime W = 0.9486, p-value = 0.05751

And the Q-Q plot below: http://i.stack.imgur.com/AGd8u.png

Would it be safe to say I cant reject the null hypothesis that the data is normal? What would be the correct interpretation?

PS: I used R.
 

ledzep

Point Mass at Zero
#2
You can see that the distribution is slightly heavier tailed than standard normal. So, the assumption of normality is suspect.
If you're strictly following the 5% level of significance, then the assumption is normality is fine. The p-value is borderline. What would you have done if the p-value was 0.04751? How is 0.05751 different from 0.04751?
As the plot says there seem to be slightly heavier tail. So, you may want to report this fact. But if you've already defined to judge the significance strictly at 5% level, you will be alright.
 
#3
Intesting,
Say the data is that of goal scored time in a football game.
and say I have a calculated the mean of 50.07.

What would be my null hypothesis?
 

ledzep

Point Mass at Zero
#4
What would be my null hypothesis?
I can't tell what your null is.
The null depends on your objective and you haven't told me what your objective is.
What do you want to test here? The mean time for first goal is >50 mins, < 50 mins or something else?