Question

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.

Answer 1

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

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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)

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