STAT1020 Statistical Reasoning and Literacy

Question 1 – Eating Habits and Sport

It has been established that Healthy eating habits of school age children impacts on all aspects of their life. A study examined the effect of healthy eating habits on the level of participation of primary school children in team sports.

a)What is the probability of a student participating in team sports?
b)What is the probability of a randomly student having healthy eating habits and participating in team sports?
c)What is the probability that a student has healthy eating habits or participates in team  sports
d)What is the probability of a student participating in team sports given that they have healthy eating habits? 
e)What is the probability of a student participating in team sports given that they do not have healthy eating habits?
f)Based on your responses to parts d and e, do EATING HABITS APPEAR TO impact participation in team sports?

Question 2 – The Language Structure Index

The language structure index is a component used in the CELF-4 test

“The Language Structure index is an overall measure of receptive and expressive components of interpreting and producing sentence structure. This index is used only for students ages 5 – 8 years.”

The language structure index has a mean score of 110 and a standard deviation of 5. Use the empirical rule (68 – 95 – 99.7% rule) to answer the following questions:

a)What is the probability that a student receives a score that is more than 115?
b)What is the probability that a student receives a score of between 105 and 120?
c)What mark does a student need to attain so that they are in the top 2.5% of student scores?

Question 3 – Vegetables & Weight loss

A researcher randomly selects a sample of 300 diabetic adults who are overweight and aged 20 years or more who do not regularly eat vegetables. The researcher assigns 150 of these adults to a diet that includes at least 50% vegetables for each meal. The remaining 150 participants continue with their regular diets. Prior to their allocation, the weight of each participant is recorded. After 6 months the researcher records their weight in kg and a comparison is made between the pre-study levels and the post-study levels of weight.

a)Is this an observational or an experimental study? Briefly justify your answer.

b) Identify the explanatory (X) variable and the response (Y) variable. Briefly justify your answer.

c) The data revealed that, for those on the diet with 50% vegetables, the reduction in weight was, on average, 6 kg. For those who do not eat vegetables regularly, the reduction in weight was, on average, 1 kg. What is the most appropriate hypothesis test to use to determine whether a diet rich in vegetables is significantly more effective in reducing weight compared to a diet without vegetables as a main part of diet?

d)State the null hypothesis and the alternative hypothesis for the proposed test.

e)What do the summary statistics presented in part c) suggest about the effectiveness of the vegetable rich diet? Are these figures enough to make a conclusive statement about the researcher’s hypotheses? Explain why or why not

f)Assume the hypothesis test resulted in a p-value of 0.02. Make a conclusion based on this p-value. Include a statement of how you reached this decision based on the hypotheses you described in part d). Use a level of significance of 0.05 for this test.