Question

13. When the rod shearing process at Newcastle Steel is ‘in control’ it produces rods with a mean length of 120 cm. Periodically, quality control inspectors select a random sample of 36 rods. If the mean length of sampled rods is too long or too short, the shearing process is shut down. The last sample showed a mean of 120.3 cm with a standard deviation of 0.9 cm. Using α = 0.05, the appropriate decision is _________.

    1. do not reject the null hypothesis and shut down the process

    2. do not reject the null hypothesis and do not shut down the process

    3. reject the null hypothesis and shut down the process

    4. reject the null hypothesis and do not shut down the process

Answer 1

The provided sample mean is 120.3 120.3 and the sample standard deviation is 0.9, and the sample size is n = 36.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 120

Ha: μ ≠​ 120

(2) Rejection Region

Based on the information provided, the significance level is α = 0.05, and the critical value for a two-tailed test is t_c = 2.03.

(3) Test Statistics

The t-statistic is computed as follows:

  

(4) Decision about the null hypothesis

Since it is observed that |t| = 2 < t_c = 2.03, it is then concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is different than 120, at the 0.05 significance level.

the appropriate decision is do not reject the null hypothesis and do not shut down the process