Question

In: Statistics and Probability

In a shoe factory, two machines are used. A random sample of 11 shoes manufactured on...

In a shoe factory, two machines are used. A random sample of 11 shoes manufactured on machine A, and a sample of 21 shoes manufactured on machine B gave the following results. the results in relation to the length of the shoes is:

machine   average length Standard deviation

A 4.95 cm 0.13 cm

B    5.01 cm 0.15 cm

total shoe length >4.5 9 8

prove with 95% that the difference between the actual average length of the shoes produced by the two machines is greater than 5

Solutions

Expert Solution

Solution:

• Hypothesis for given problem is:

Ho: u1 - u2=5 vs Ha: u1 - u2 > 5

Now, we have to prove that the difference between the actual average length of the shoes produced by the two machines is greater than 5. i.e. we have to reject Ho.

We prove this using 95% CI:

Hence, 95% CI does not contain 5 i.e. it means that we Reject Ho.

Therefore, The difference between the actual average length of the shoes produced by the two machines is greater than 5.

orchestra answered 2 years ago
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