Question

A Manufacturing group mass produces one product. It has 10 manufacturing locations and the manager of each location only reports the average quantity made per location each week. There are 9 production lines per location and each average reported is made up of one individual data point per production line. The Corporate Operations Manager claims to have made improvements that increased output.

The historical corporate-wide output reported per line is 10,510 units with a standard deviation of 450 units.

The Corporate Operations Manager claims that his lean events have increased output.

A corporate-wide sample was reported the next week and the average reported was 11,020 units per line.

Can the Corporate Operations Manager claim an increase in the performance of the historical average based on the week reported for production per line based on a statistical significance level of 1%?

*Use and show the 5-step process.

Use Z or t values , not p-values

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 10510
Alternative Hypothesis: μ ≠ 10510

Rejection Region
This is two tailed test, for α = 0.01
Critical value of z are -2.58 and 2.58.
Hence reject H0 if z < -2.58 or z > 2.58

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (11020 - 10510)/(450/sqrt(90))
z = 10.75

P-value Approach
P-value = 0
As P-value < 0.01, reject the null hypothesis.

Rejection Region Approach
As the value of test statistic, z is outside critical value range, reject the null hypothesis.

There is significant evidence to conclude that the performance has increased.