Question

Please use only Minitab or Excel. Thank you

Please use only Minitab or Excel. Thank you

Two different tire compound formulas are tested for tire wear in thousandths of inches. Everything else that might vary is held at a pre-determined constant value to the best of the experimenter's ability. The following are the samples randomly selected from the tires made by the different compound formulas (assume the outcomes are normally distributed). The values in the table are the wear in thousandths inches. The design engineer claims that Compound Formula 1 will result better product. Perform the adequate analysis and comment on the design engineer's statement. Sample id Compound Formula 1 Compound Formula 2 72 74 75 76 75 75 78 72 74 74 78 82 82 81 80 72 78 74 73 13 14 15 16 17 18 19 20 21 78 76 75 72 73 73 81 23 24 25 26 27 28 29 30 78 75 72 76 74 79 76 76 75 81 76 82 72

Please use only Minitab or Excel.

Please use only Minitab or Excel.

Thank you

Answer 1

Claim: Compound formula 1 will result better product.

Null and alternative hypothesis is

$H0:\mu1\leq \mu2$ Vs    $Ha:\mu1> \mu2$

For doing this test first we have to check the two groups have population variances are equal or not.

Null and alternative hypothesis is

$H0:\sigma _{1}^{2}=\sigma _{2}^{2}$

$Ha:\sigma _{1}^{2}\neq \sigma _{2}^{2}$

Test statistic is

F = largest sample variance / Smallest sample variances

F = 4.7310 / 4.3264 = 1.09

Degrees of freedom => n1 - 1 , n2 - 1 => 30 - 1 , 30 - 1 => 29 , 29

Critical value = 1.86 ( Using f table)

Critical value > test statistic so we fail to reject null hypothesis.

Conclusion: The population variances are equal.

So we have to use here pooled variance.

By using Excel we can solve this question easily.

Path is Click on Data ----------> Data Analysis ----------> t-Test: Two samples assuming equal variance ----->

Variable range 1 : Select compound formula 1 values

Variable range 2 : Select compound formula 2 values

Hypothesized differenced value: 0

Alpha: 0.05

Output Range: select an empty cell.

We get

t-Test: Two-Sample Assuming Equal Variances
	Compound Formula 1	Compound Formula 2
Mean	74.46667	78.4
Variance	4.326437	4.731034
Observations	30	30
Pooled Variance	4.528736
Hypothesized Mean Difference	0
df	58
t Stat	-7.15843
P(T<=t) one-tail	7.94E-10
t Critical one-tail	1.671553
P(T<=t) two-tail	1.59E-09
t Critical two-tail	2.001717

So p-value is near about 0

So p-value < 0.05 we reject null hypothesis.

Conclusion: Compound formula 1 will result better product.