Number 2 **Statistical Testing in Manufacturing**Managers at an automobile manufacturing plant are interested in examining the mean completion time, \( \mu \), of an assembly line operation. Historical data suggests the mean completion time is 41 minutes. However, there is reason to believe this time has increased, prompting a statistical test.A random sample of completion times gave a sample mean of 42 minutes. The population's completion time standard deviation is assumed unchanged from a previous value of 5 minutes.### ProblemBased on the information, complete the following:#### (a) Hypotheses FormulationIdentify the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \):- \( H_0 \): \( \mu = 41 \)- \( H_1 \): \( \mu > 41 \)#### (b) Error AnalysisIf managers do not reject the null hypothesis, what kind of error may occur?- **Type II Error**: Failing to reject the null hypothesis when it is actually false.#### (c) Type II Error ExplanationAssume the true mean completion time for the assembly line is 44 minutes. Fill in the blanks to describe a Type II error:- A Type II error would be **failing to reject** the hypothesis that \( \mu \) is **41** when, in fact, \( \mu \) is **44**.

The hypothesized mean is 41 minutes.

Managers at an automobile manufacturing plant would like to examine the mean completion time, μ, of an assembly line operation. The past data indicate that the mean completion time is 41 minutes, but the managers have good reason to believe that this value has increased. The managers plan to perform a statistical test. After choosing a random sample of assembly line completion times, the managers compute the sample mean completion time to be 42 minutes. The standard deviation of the population of completion times can be assumed not to have changed from the previously reported value of 5 minutes. Based on this information, complete the parts below. (a) What are the null hypothesis H₁ and the alternative hypothesis H₁ that should be used for the test? Ho (b) Suppose that the managers decide not to reject the null hypothesis. What sort of error might they be making? (Choose one) ▼ (c) Suppose the true mean completion time for the assembly line operation is 44 minutes. Fill in the blanks to describe a Type II error. 3 O