Two different alloys are being considered for making lead-free solder used in th

Question

Two different alloys are being considered for making lead-free solder used in the wave soldering process for printed circuit boards. A crucial characteristic of solder is its melting point, which is known to follow a Normal distribution. A study was conducted using a random sample of 21 pieces of solder made from each of the two alloys. In each sample, the temperature at which each of the 21 pieces melted was determined. The mean and standard deviation of the sample for alloy 1 were = 218.9°C and = 2.7°C; for alloy 2, the results were = 215.5°C and = 3.6°C.
1. (7) An approximate 96% confidence interval for the mean difference would be
a. 3.4 ± 2.197
b. 3.4 ± 2.123
c. 3.4 ± 2.189
d. 3.4 ± 2.197
e. 3.4 ± 2.189

2. (7)If we were to test H0: against Ha: , what would be the value of the test statistic??
a. t(20) = 3.47
b. t(20) = 8.13
c. t(21) = 3.47
d. t(21) = 2.20
e. t(40) = 3.46

3. (3)What is the approximate P-value for this test?
a. Less than 0.002
b. Between 0.001 and 0.0025
c. Less than 0.001
d. Between 0.002 and 0.005

Explanation / Answer

Ans:

1)critical t value=tinv(0.04,40)=2.123

96% confidence interval for difference

=(218.9-215.5)+/-2.123*SQRT((2.7^2/21)+(3.6^2/21))

=3.4+/-2.123*SQRT((2.7^2/21)+(3.6^2/21))

2)df=21+21-2=40

Test statistic:

t(40)=(218.9-215.5)/SQRT((2.7^2/21)+(3.6^2/21))

t(40)=3.46

Option e is correct.

3)

p-value(one tailed)=tdist(3.46,40,1)=0.0006

p-value(2 tailed)=tdist(3.46,40,2)=0.0012

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