Question

Two processes in a manufacturing line are performed manually: operation a and operation b. a random sample of 50 different assemblies using operation a shows that the sample average time per assembly is 8.05 minutes, with a population standard deviation of 1.36 minutes. a random sample of 38 different assemblies using operation b shows that the sample average time per assembly is 7.26 minutes, with a population standard deviation of 1.06 minutes. for alpha = 0.10, the test statistics (z-value) would be _____. (specify your answer to the 2nd decimal.)

Answer 1

The test statistic (z-value) for operation b is approximately 1.28.

Step-by-step explanation:

The test statistic (z-value) can be calculated using the formula:

z = (X - μ) / (σ / sqrt(n))

1. For operation a, the sample size (n) is 50. The sample mean (X) is 8.05 minutes, and the population standard deviation (σ) is 1.36 minutes. The population mean (μ) is not provided.
2. For operation b, the sample size (n) is 38. The sample mean (X) is 7.26 minutes, and the population standard deviation (σ) is 1.06 minutes. The population mean (μ) is not provided.
3. To calculate the test statistic for operation a, we need to know the population mean. Without that information, we cannot calculate the z-value.
4. To calculate the test statistic for operation b, we can use the given values:

z = (7.26 - μ) / (1.06 / sqrt(38))

Since alpha = 0.10, we find the corresponding z-value from the z-table or use a calculator. The z-value at alpha = 0.10 is approximately 1.28. Therefore, the test statistic (z-value) would be approximately 1.28.