Question

 Bottles that carry carbonated soda underwent a makeover. Suppose researchers want to test the bursting strength of these designs to make sure no one loses a hand or something. 10 random samples from the old design and 10 random samples from the new design were taken. The strengths of the bottles are given in the table below. Note that these designs are independent of each other

 Old design 210 212 211 211 190 213 212 211 164 209 

 New design 216 217 162 137 219 216 179 153 152 217 

Perform the appropriate nonparametric test to determine bursting strength on the new design is larger than that of the old design. Use α = 0.025 

Answer 1

First enter Data into EXCEL

We have to find the sample mean.

Excel command is =AVERAGE(Select data)

Now we have to find sample standard deviation.

Excel command is =STDEV(Select data)

s1 = 15.678

s2 = 33.459

n1= 10

n =10

s1 = 15.678

s2 = 33.459

Claim : Bursting strength on the new design is larger than that of the old design

Null and alternative hypothesis is

Vs

Level of significance = 0.025

Before doing this test we have to check population variances are equal or not.

Null and alternative hypothesis is

Vs

Test statistic is

F = Larger variance / Smaller variance =1119.505 / 245.780 = 4.5545

Degrees of freedoms

Degrees of freedom for numerator = n1 - 1 = 10 - 1 = 9

Degrees of freedom for denominator = n2 - 1 = 10 - 1 = 9

Critical value = 4.026 ( using f-table )

F test statistic > critical value    we reject null hypothesis.

Conclusion: Population variances are unequal.

So we have to use unpooled variance.

Formula

u1 – u2 = 0                  (Assume H0 is True )

d.f = n1 + n2 – 2 = 10 +10 - 2 = 18

p-value =0.9242 ( using t table )

p-value ,Failed to Reject H0

conclusion :At There is a insufficient evidence to conclude that the Bursting strength on the new design is larger than that of the old design