Statistical analysis has shown a strong positive correlation between the number of people who drown in pools and the number of films in which Nicolas Cage appears.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1) It was reported that the mean household income in the U.S. was $72,641, while the median household income was $51,939 in 2013. The mean was also reported to grow faster than the median during the period between 1970 and 2015. How can this difference between mean and median numbers and their trends be interpreted? What is the shape of the income distribution and, provided that the current trends continue, what is the future income distribution likely to be?

2)Statistical analysis has shown a strong positive correlation between the number of people who drown in pools and the number of films in which Nicolas Cage appears. The correlation is and the R = 0.67 (R2=0.44). Does that mean that Nicolas Cage causes people to drown?

3)For your research, you have purchased a scale, which has a declared accuracy with a standard deviation of 0.2gms for the range of weights that it usually measures. To test whether the scale operates correctly, a standard 5gms weight is chosen and 21 independent weight measurements are taken. The results of this experiment are as below.

 

4.7	5.3	5.1	5	5.1	5.1	4.7	4.9
4.7	5.3	4.8	5.2	4.9	5.2	5.1	5
5	4.9	4.7	5	4.6

1.     Find the sample mean and sample variance for these data. (5 Marks)

2.     Confirm if the variance seems consistent with the known standard deviation of 0.2gms (just a comment is sufficient). (3 Marks)

3.     By using the result in part (a), show the appropriate distribution for the mean. (5 Marks)

4.     How reasonable is it to assume that the balance operates correctly? (Hint: Formulate a hypothesis and test it.) (10 Marks)

5.     Find 95% and 99% confidence intervals for the weight being measured. (Consider the fact that we know the true weight for this case.) What distribution do you use? (7 Marks) 

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