Question

In: Statistics and Probability

Jason believes that the sales of coffee at his coffee shop depend upon the weather. He...

Jason believes that the sales of coffee at his coffee shop depend upon the weather. He has taken a sample of 5 days. Below you are given the results of the sample.

Cups of Coffee Sold

Temperature

700

50

500

60

400

70

200

80

100

90

Now we are going to conduct a hypothesis test to see if there is a significant relationship between sales of coffee and temperature.

The hypotheses are:

H 0 ; β 1 = 0

What is sb1? Give two decimal places in your answer if necessary.

Solutions

Expert Solution

x y (x-x̅)² (y-ȳ)² (x-x̅)(y-ȳ)
50 700 400.0000 102400.0000 -6400.000
60 500 100.0000 14400.0000 -1200.000
70 400 0.0000 400.0000 0.000
80 200 100.0000 32400.0000 -1800.000
90 100 400.0000 78400.0000 -5600.000
ΣX ΣY Σ(x-x̅)² Σ(y-ȳ)² Σ(x-x̅)(y-ȳ)
total sum 350.00 1900.00 1000.00 228000.00 -15000.00
mean 70.00 380.00 SSxx SSyy SSxy

sample size ,   n =   5          
here, x̅ = Σx / n=   70.000   ,     ȳ = Σy/n =   380.000  
                  
SSxx =    Σ(x-x̅)² =    1000.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   -15000.0          
                  
estimated slope , ß1 = SSxy/SSxx =   -15000.0   /   1000.000   =   -15.0000
                  
intercept,   ß0 = y̅-ß1* x̄ =   1430.00000          
                  
so, regression line is   Ŷ =   1430.00   +   -15.000   *x

-=======================

Ho:   ß1=   0          
H1:   ß1╪   0          
n=   5              
alpha =   0.05              
estimated std error of slope =Se(ß1) = Se/√Sxx =    31.623   /√   1000.00   =   1.00 (answer)

please revert for doubts and
please UPVOTE the solution


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