A precision engineering plant fills high-pressure gas cylinders to a volume, $V\,$ mL, which follows a normal distribution $N(μ,122)N(\mu, 12^2)$ . To monitor the consistency of the filling process, a random sample of $n\,$ cylinders is selected and tested at the 1% level of significance using the following hypotheses:

H_0 : \mu = 1500 \quad \text{and} \quad H_1 : \mu < 1500

Find, in terms of $n$ , the critical region of the test.

The probability of a Type II error, when the true mean is $μ=1490\mu = 1490$ , is less than 0.05.

Find the minimum value of $n$ .

H_0 : \mu = 1500 \quad \text{and} \quad H_1 : \mu < 1500

Find, in terms of $n$ , the critical region of the test.

The probability of a Type II error, when the true mean is $μ=1490\mu = 1490$ , is less than 0.05.

Find the minimum value of $n$ .

2 Statistics

Question 269

Markscheme

2 Statistics

Question 269

Markscheme

2 Statistics

Question 269

2 Statistics Questions

2 Statistics

Question 269

2 Statistics Questions