Question

A tire manufacturing plant produces 15.2 tires per hour. This yield has an established variance of 2.5 (standard deviation of 1.58 tires/hour). New machines are recommended, but will be expensive to install. Before deciding to implement the change, 12 new machines are tested. They produce 16.8 tire per hour. Is it worth buying the new machines? Use alpha value of 0.10.

Answer 1

=18.2, =1.58 n= 12, =16.8 , = 0.10

Ho: = 15.2

Ha: > 15.2

calculate critical value for right tailed test with = 0.10

using normal z table we get

Critical value= 1.282

formula for test statistics is

z = 3.51

test statistics = 3.51

calculate p-Value

p-Value = 1 - P( z < 3.51)

find P( z < 3.51) using normal z table we get

P( z < 3.51) = 1

p-Value = 1-1

P-Value = 0

Since, test statistics ( z ) = 3.51 > 1.282,

Hence, Null hypothesis is rejected.

Conclusion"

Therefore there is sufficient evidence to support the claim that, it is worth buying the new machines