Asked by Kandace Stagg on May 08, 2024
Verified
A lathe is set to cut bars of steel into lengths of 6 centimeters.The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 centimeters.A sample of 121 bars is selected randomly and measured.It is determined that the average length of the bars in the sample is 6.08 centimeters with a standard deviation of .44 centimeters.
a.
Formulate the hypotheses to determine whether or not the lathe is in perfect adjustment.
b.
Compute the test statistic.
c.
Using the p-value approach, what is your conclusion? Let α = .05.
Test Statistic
A calculated value from sample data, used to decide whether to reject the null hypothesis in the context of a hypothesis test.
Null Hypothesis
In statistical testing, a hypothesis that assumes there is no significant difference or effect, serving as the default assumption to test against.
- Obtain insight into the strategy for framing null and alternative hypotheses for numerous statistical analyses.
- Execute the computation of test statistics for multiple types of data and study frameworks.
- Master the notion of p-value along with its calculation procedures.
Verified Answer
SP
Shreyan PatelMay 13, 2024
Final Answer :
a.
H0: μ = 6 centimeters
Ha: μ ≠ 6 centimeters
b.
t = 2
c.
p-value (.0456) is between .02 and .05; therefore, reject H0. The lathe is not in perfect adjustment.
a.
H0: μ = 6 centimeters
Ha: μ ≠ 6 centimeters
b.
t = 2
c.
p-value (.0456) is between .02 and .05; therefore, reject H0. The lathe is not in perfect adjustment.
Learning Objectives
- Obtain insight into the strategy for framing null and alternative hypotheses for numerous statistical analyses.
- Execute the computation of test statistics for multiple types of data and study frameworks.
- Master the notion of p-value along with its calculation procedures.