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In a study of Americans from a variety of professions were asked if they considered themselves left-handed, right-handed, or ambidextrous. The results are given below: Profession Right Left Ambidextrous Total Psychiatrist 101 10 7 118 Architect 115 26 7 148 Orthopedic Surgeon 121 6. 132 Lawyer 83 16 105 Dentist 116 10 6 132 Total 536 67 32 635 a) Amongst Americans, 10% of the population is left-handed. Is there enough evidence from this data to show that more than 10% of those in these professions are left-handed? Make sure you show all the steps of this test. b) Construct and interpret the 99% confidence interval for the proportion of Americans who are ambidextrous, based on this sample. c) Is there enough evidence to conclude that proportion of left-handed orthopedic surgeons is less than the proportion of left-handed architects? Make sure you show all the steps of the test.

A machine produces metal discs with a diameter of 12cm. The diameters of discs need to be exactly 12cm with only a small variation of 2%. On a particular day, the manufacturing manager measured the diameters of 50 discs and noted that the mean is 11.5cm. It is assumed that the diameters of discs are normally distributed with a standard deviation of 1.8cm. Conduct a hypothesis testing using the critical value approach, at the 0.1 level of significance. Is there evidence that the machine is not producing the discs at the specified diameter of 12cm?

The production machines of a company produce metal discs of 200g. It is noted that the weight of the discs follows a normal distribution with a standard deviation of 7g. To test the consistency of the machines, 50 discs are randomly selected and the mean weight is 205g. What is the 99% confidence interval for the average weight of the selected discs?

A certain brand of yogurt is packed in tubs with masses that are normally distributed with mean of 1kg and a standard deviation of 50g. (a) Find the probability that a randomly selected tub weighs i. More than 950g, il. Between 950g and 1100g. (b) A box contains 20 such tubs. What is the probability that the mean mass for a tub is between 980g and 1030g?

A remotivation team in a psychiatric hospital conducted an experiment to compare five methods for remotivating patients. Patients were grouped according to level of initial motivation. Patients in each group were randomly assigned to the five methods. At the end of the experimental period the patients were evaluated by a team composed of a psychiatrist, a psychologist, a nurse, and a social worker, none of whom was aware of the method to which patients had been assigned. The team assigned each patient a composite score as a measure of his or her level of motivation. The results were as follows: Level of Initial Motivation Remotivation Method A D E Nil 58 68 60 68 64 Very low Low 62 70 65 80 69 67 78 68 81 70 Average 70 81 70 89 74 Do these data provide sufficient evidence to indicate a difference in mean scores among methods? a. What experimental design is most appropriate to use? b. What is factor being considered in the study? c. How many levels are there in the given factor?