A manufacturer claims that the probability that one of its sensors passes a calibration check is 0.70. An engineer believes that the probability is greater than 0.70. The engineer will test n n\,n independently selected sensors and will reject the null hypothesis only if every sensor passes.
State suitable hypotheses.
Find the least value of n n\,n for which this test has a significance level below 1%.
The least possible value of n n\,n is used and every sensor passes. Complete the test.