Can someone please explain for part B how you get from -2.508 to the P-value of
ID: 3296229 • Letter: C
Question
Can someone please explain for part B how you get from -2.508 to the P-value of 0.0203? I tried using the T-table and Z-tables and I just don't understand where that number in coming from. I see 1.415 when I look up df=7 for 10% for a 1 tailed test on a T table.
Popcorn Yvon Hopps ran an experiment to test optimum power and time settings for microwave popcorn. His goal was to find a combination of power and time that would deliver high-quality popcorn with less than 10% of the kernels left unpopped, on average. After experimenting with several bags, he determined that power 9 at 4 minutes was the best combination. a) He concluded that this popping method achieved the 10% goal. If it really does not work that well, what kind of error did Hopps make? b) To be sure that the method was successful, he popped 8 more bags of popcorn (selected at random) at this setting. All were of high quality, with the following percentages of uncooked popcorn: 7, 13.2, 10, 6,7.8,2.8,2.2,5.2. Does this provide evidence that he met his goal of an average of no more than 10% uncooked kernels? Explain.Explanation / Answer
We have to use t distribution here because population standard deviation is unknown.
Test statistics = -2.508
DF = n - 1 = 7
We can not find exact p- value using table.
Let's use excel,
It is one tailed test ( Left tailed )
P-value for left tailed test is,
p-value = P( t < test statistics ) = P( t < -2.508 )
Usinge Excel, =t.dist( t, df, 1 ) This function returns cumulative probability.
P( t < -2.508 )
=t.dist( t, df, 1 )
=t.dist( -2.508, 7 , 1 ) = 0.0203
p-value = 0.0203