[15 pts] A manufacturing process produces machine parts with measurements. The standard deviation of these measurements must be no more than 0.52 MI. A random sample of 20 parts in a given lot revealed a standard deviation in measurement of 0.568. Is there sufficient evidence at a = 0.05 to conclude that the variance of the parts is outside the required guidelines? [2 pts] State the null and alternative hypotheses. [3 pts] Find the test statistic. [3 pts] Find the final critical value(s). [2 pts] Make the decision. [2 pts] Calculate the p-value using R. [2 pts] Make the decision based on the p-value.
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Null hypothesis: The variance of the parts is within the required guidelines (σ^2 ≤ 0.52^2). Alternative hypothesis: The variance of the parts is outside the required guidelines (σ^2 > 0.52^2). Show more…
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A manufacturing process produces machine parts with measurements the standard deviation of which must be no more than 0.52 mm. A random sample of 20 parts in a given lot revealed a standard deviation in measurement of 0.568 Is there sufficient evidence at α = 0.05 to conclude that the standard deviation of the parts is outside the required guidelines? Apply the following statistical testing methods to justify your answer. i. Traditional method ii. P-value method
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A manufacturing process produces machine parts with measurements. The standard deviation of these measurements must be no more than 0.52mm. A random sample of 40 parts in a given lot revealed a standard deviation of 0.568mm. Is there sufficient evidence at Alpha= 0.05 to conclude that the standard deviation of the parts is outside the required guidelines?
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23. A machined engine part produced by a certain company is claimed to have a diameter variance no larger than 0.0002 inch. A random sample of ten parts gave a sample variance of 0.0003. Assuming normality of diameter measurements, is there significant evidence to refute the company's claim? Use α = 0.05. Use critical value method or p-value method. (a) Clearly mention the hypotheses to be tested. [1] (b) Clearly specify the test statistic, its distribution and its value. [1] (c) Clearly specify the critical value/p-value. [1] (d) Clearly mention your conclusion based on the context of the problem. [1]
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