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The developer of a new welding rod claims that spot welds using his product will have greater strength than conventional welds. For 45 welds using the new rod, the average tensile strength is 23,500 pounds per square inch, with a standard deviation of 600 pounds. For 40 conventional welds on the same materials, the average tensile strength is 23,140 pounds per square inch, with a standard deviation of 750 pounds. Using the 0.01 level, what is the calculated value of t statistic? (Specify your answer to the 3rd decimal.)

Respuesta :

JeanaShupp

Answer: 2.424

Step-by-step explanation:

As per given , we have

For [tex]n_1=45[/tex] ,

sample mean : [tex]\overline{x}_1=23500[/tex]

Sample standard deviation : [tex]s_1= 600[/tex]

For [tex]n_2=40[/tex] ,

sample mean : [tex]\overline{x}_2=23140[/tex]

Sample standard deviation : [tex]s_2= 750[/tex]

Test statistic :

[tex]t=\dfrac{\overline{x}_1-\overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2}}}[/tex]

i.e. [tex]t=\dfrac{23500-23140}{\sqrt{\dfrac{600^2}{45}+\dfrac{750^2}{40}}}[/tex]

Simplify , we get

[tex]t=\dfrac{360}{148.535}=2.42367922035\approx2.424[/tex]

Hence,  the calculated value of t statistic= 2.424

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