Question

1. The quality of coffee is to be gauged by two coffee tasters. They apply a rating from 0 to 10 (with good coffee rated 10, poor coffee rated 0). The coffee has been perked from 1 to 8 minutes. The regression equation is y=1.01x-.55. What taste value do you expect for coffee perked 5 minutes, 7 minutes, 11 minutes?

2. Is there a correlation between the minutes the coffee is perked and the taste value? There were 16 pairs with a correlation coefficient of .875.

*please state the null and alternate hypothesis for this problem* Also if possible can you format the answer in a 7 step layout like this
1) Null Hypothesis
2) Alternative Hypothesis
3)Alpha Level
4) Reject Ho if....
5) Use the proper formula to calculate the answer
6) Reject or don't reject
7) Summarize the decision

*Thank you so much in advance!!*

Answer 1

1. We have, y= 1.01x - 0.55

Putting x=5 here we get, y= 1.01*5 - 0.55= 4.5

Putting x= 7, y= 1.01*7 - 0.55= 6.52

Putting x=11, we get, y= 1.01*11- 0.55= 10.56

2. We are testing,

1)H0: p= 0 vs

2)H1:p is not equal 0

3) Level of Significance= 0.05

4) n=16 so df= n-2= 14 so critical value: 0.426

So rejection region is r>0.426

5) given, r= 0.875 so we can see that r value >0.426

6) From 5, above we see that we have sufficient evidence to Reject H0.

7) So we can conclude that p is not to 0 at the 5% level of significance, ie yes there is a correlation between the minutes the coffee is perked and the taste value.