A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0: μ = 12 against H1: μ < 12, using a random sample of four specimens. (a) What is the type I error probability if the critical region is defined as x < 11.5 kilograms? (b) Find β for the case in which the true mean elongation is 11.25 kilograms. (c) Find β for the case in which the true mean is 11.5 kilograms.
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rafikiedu09 3 weeks ago
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The Type I error's computed value is 0.02275 and The Type II error has a computed value of 0.50 based on probability.

What is probability?

• The potential or opportunity of an event happening is known as probability.
• The probability is equal to the variety of possible outcomes. the estimated number of outcomes that could occur.

(a) Type I error probability if the critical region is defined as x < 11.5 kilograms  The Type I error's computed value is 0.02275.

Observe that there is a 2.275% likelihood of dismissing the null hypothesis if it is true based on the Type I error probability.

(b) β for the case in which the true mean elongation is 11.25 kilograms.  The Type II error's computed value is 0.1587.

Observe that there is a 15.87% possibility of refusing to disprove the null hypothesis when it is untrue based on the Type II error probability.

(c)  β for the case in which the true mean is 11.5 kilograms.  The Type II error has a computed value of 0.50.

Observe that there is a 50% possibility of neglecting to disprove the null hypothesis when it is untrue based on the Type II error probability.