Mrs. Pellegrin has weighed 5 packages of cheese and recorded the weights as 10.2 oz, 10.5 oz, 9.3 oz, 9.8 oz, and 10.0 oz. She calculated the standard deviation to be 0.45 oz. The cheese factory lists the package weight at 10 oz. t equals fraction numerator x with bar on top minus mu over denominator begin display style bevelled fraction numerator s over denominator square root of n end fraction end style end fraction The t-statistic for a two-sided test would be .

- 0.20

Step-by-step explanation:

Given the following :

Sample weights 10.2, 10.5, 9.3, 9.8, 10

Sample mean: ΣX / n

n = number of observations = 5

Sample mean (m)= (10.2+10.5+9.3+9.8+10) / 5= 49.8 / 5 = 9.96

Population mean (p) = 10.0

Standard deviation (sd) = 0.45

T statistic = (m - p) / sd/sqrt(n)

Tstatistic = (9.96 - 10) / 0.45÷sqrt(5)

= - 0.04 / 0.2012461

= - 0.1987

= - 0.20

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.