AY5126: Motor vehicles have a recommended tire pressure of 32 psi. The road safety authority launches a roadside checkpoint to measure: Analytical and Communication Skills Development Assignment, NUI, Ireland

Question 1

Motor vehicles have a recommended tire pressure of 32 psi. The road safety authority launches a roadside checkpoint to measure the actual tire pressure in the front left tire of a random sample of 50 passing cars. The authority hopes to use this information to decide whether an additional investment in air pumps is required at filling stations

• Define the population characteristic of interest in the above example.
• The following SPSS output has been produced from a one-sample t-test. Using the 5-step approach to hypothesis testing, determine whether the road safety authority should invest in additional air pumps at filling stations.

• The following 95% confidence interval has been computed for the mean tire pressure of all motor vehicles. Does the confidence interval support the conclusion you made in part (b)? Explain your answer in detail.

• Assume that the median tire pressure of all motor vehicles is 32.82. Produce an appropriate graph that gives an approximation of the likely distribution of the tire pressure variable.
• Redraw the graph assuming that the median tire pressure of all motor vehicles is actually 34.
• Comment on the graph in part and provide an example of a dataset that would likely follow a similar distribution.

Question 2

Political science students at a university carry out a survey of 1,669 randomly selected registered voters. They wish to determine if there is an association between the respondents’ political party and their opinion about a newly proposed gun control law. The following two-way table summarizes the count data.

• Among those who are democrats, what percentage supports the newly proposed law?
• Among those who are republicans, what percentage supports the newly proposed law?
• Do your calculations in parts (a) and (b) indicate that there is an observed relationship between political party and opinion about the gun control law? Explain your answer.
• Assuming that a relationship between the two variables is observed in the sample, can the political science students infer from this that there is a relationship in the population? If not, how would they go about making this inference?

The economic and social research institute has gathered data on the potential factors that influence current salary levels in the market. The following statistical output has been produced from linear regression, with current salary as the response variable and education and previous experience as the explanatory variables.

• Does an individual’s education predict their current salary well? Explain your answer with specific reference to both the p-value of 0.000 and the beta coefficient of 4020.343.
• Provide an example of a possible confounding variable that might change your
  interpretation in part (e). Explain your answer.
• What would influence your conclusion on whether an individual’s previous experience is significantly related to their current salary? Explain your answer in detail.

Question 3

The department of health is currently drafting a new health initiative to promote weekly exercise. The department wants to identify which groups in society most need additional support to increase their amount of weekly exercise. The department issues a survey to a random sample of 100 employed individuals asking them “How many minutes do you typically exercise in a week?” The summary statistics from the sample are:

• Suggest an appropriate statistical test that would provide useful information to allow the department to identify where supports are most needed in the population. Explain your answer.
• Assuming a p-value of 0.073, write out the approach to the statistical test you suggested in part (a). Clearly state your conclusion.
• Based on your conclusion in part (b), what recommendation would you make to the department of health regarding which group most needs additional support to increase their amount of weekly exercise. Explain your answer.
• Assume that the department of health gathers additional data on the minutes of weekly exercise from the third group in society:

Suggest an appropriate statistical test that would allow for this additional data to be incorporated into the previous analysis.

• Assume that the distribution of weekly exercise in minutes is bell-shaped. Using the Empirical Rule, explain whether or not it would be unusual for an unemployed individual to exercise for the same amount of time as an average individual employed in a high-income job.