Question

A stress analysis was conducted on random samples of epoxy-bonded joints from two species of wood. A random sample of 120 joints from species A had a mean shear stress of 1250 psi and a standard deviation of 350 psi, and a random sample of 90 joints from species B had a mean shear stress of1400 psi and a standard deviation of 250 psi. Find a 98% confidence interval for the difference in mean shear stress between the two species

Answer 1

Answer: Our required 98% confidence interval would be (53.51,246.49).

Explanation:

Since we have given that

Sample of joints from species A = 120

Mean of shear stress = 1250 psi

Standard deviation = 350 psi

Sample of joints from species B = 90

Mean = 1400 psi

Standard deviation = 250 psi

98% confidence interval

α = 100 -98 = 2%

`(\alpha)/(2)=(2)/(2)=1\%\\\\z_{(\alpha)/(2)}=2.33`

98% confidence interval would be

`(1400-1250)\pm 2.33\sqrt{(350^2)/(120)+(250^2)/(90)}\\\\=150\pm 2.33* 41.41\\\\=(150-96.49,150+96.49)\\\\=(53.51,246.49)`

Hence, our required 98% confidence interval would be (53.51,246.49).