1) An aeronautics researcher of an airplane manufacturer compared the cruising speed of a sample of 80 planes fitted with the standard engine with that of a sample of 80 planes filled with a new engine designed for better fuel efficiency. At the juncture of the study, it is not known if the new engine will yield relatively higher cruising speed. The researcher wants to be 90% confident of detecting atruedifference in mean cruising speed between the two groups of planes at 5% level of significance.

Should the researcher conduct a one-sided or two-sided hypothesis test? State the null and alternative hypotheses in words. What is the power of the study? What is probability of Type I error of the study? What is the probability of Type II error of the study?(10 marks)

2)a)It is believed thatSTAT222students get less than seven hours of sleep per night, on average. The Type I error is to reject that the mean number of hours of sleep STAT222 students get per night is less than seven when, in fact, the mean number of hours of sleep STAT222 students get per night(10 marks)

i.is more than seven hours.

ii.is at most seven hours.

iii.is at least seven hours.

iv.is less than seven hours.

The correct option is __iv___.(2 marks)

b)A microbiologist is testing a water sample for E-coli. Suppose the null hypothesis,H₀, is: the sample does not contain E-coli. The probability that the sample does not contain E-coli, but the microbiologist thinks it does is 0.012. The probability that the sample does contain E-coli, but the microbiologist thinks it does not is 0.002. What is the power of this test?(8 marks)