Question 1 - Variables and Plots

A study was undertaken to investigate the link between TV programs showing violence and aggressive behaviour of teenagers from New York State (Johnson et al., Science, 2002). Researchers randomly sampled 707 teenagers from New York State. Of the 88 who watched less than one hour of TV per day, 5 were reported to have later committed an aggressive acct whilst of the 619 who watched at least one hour of TV per day, 154 were reported to have committed an aggressive act. The study gathered the following data:

Variable Name                                         Variable description

ID                                                                Unique identifier for each teenager from New York State

TV minutes                                                Number of minutes spent watching TV per day

TV usage                                                    Low = watched less than one hour of TV per day

                                                                    High = watched at least one hour of TV per day

Aggressive Acts                                        0 = No aggressive act committed

                                                                    1 = At least one aggressive act committed

a) What was the target population?

b) What was the sample?

c) What variables were recorded in this study and write down the type of each variable?

d) What would be the most appropriate graph to display the following variables?

Choose from the options of: histogram, comparative box plots, scatter plot or clustered bar charts. (1 mark: each part worth 0.5 mark)

i. Which would be the most appropriate graph to investigate the relationship between TV Usage and Aggressive Acts?

ii. Which would be the most appropriate graph to investigate the frequency distribution for TV Minutes?

Question 2 - Probabilities for Proportions

Research question: According to the US Bureau of statistics 90% of all teenagers from New York State watch TV for at least one hour per day. What is the probability that in a sample of 707 teenagers from New York State, more than 619 watched TV for at least one hour per day?

a) Calculate the following values (4dp)

Population proportion (p)= ..................................................

Sample proportion (p^)=.......................................................

b) Undertake the test for the success/ failure condition and state whether the conditions have been met:

np =.........................

nq =..........................

Therefore, the condition has been met/ not met ( circle the correct answer_.

c) If the success/ failure conditions have been met, we can adopt a normal approximation of binomial distribution for the number of teenagers from New York State who watched TV for at least one hour per day to calculate this probability. Draw the diagram of the normal distribution which you would use to answer this question. Show the position of p and p^. Shade the area of interest.

d) Complete the Excel command NORM.DIST below to show which parameters you would use to find the probability that more than 619 out of a randomly selected sample of 707 teenagers from New York State. Report the standard error to 4dp.

= 1- NORM.DIST(............,...............,................,TRUE)

e) Use the NORM.DIST command in Excel to find the probability:...............................

f) Interpret this result: