Question 1 A doctor claims that the average European is more than 8:5 kg overweight. To test this claim, a random sample of 12 Europeans were weighed, and the difference between their actual weight and their ideal weight was calculated. The data are: 14; 12; 8; 13; 1; 10; 11; 15; 13; 20; 7; 14: Assuming the data follow a normal distribution, conduct a t test to infer at the 5% significance level whether or not the doctor's claim is true. Question 2 A sample of seven is taken at random from a large batch of (nominally 12-volt) batteries. These are tested and their true voltages are shown below: 12:9; 11:6; 13:5; 13:9; 12:1; 11:9; 13:0: (a) Test if the mean voltage of the whole batch is 12 volts. (b) Test if the mean batch voltage is less than 12 volts. Question 3 In a survey of students, the number of hours per week of private study is recorded. For a random sample of 23 students, the sample mean is 18.4 hours and the sample standard deviation is 3.9 hours. Treat the data as a random sample from a normal distribution. 1 (a) Find a 99% confidence interval for the mean number of hours per week of private study in the student population. (b) Recompute your confidence interval in the case that the sample size is, in fact, 121 , but the sample mean and sample standard deviation values are unchanged. Comment on the two intervals.