Is there a difference in how males and female students perceive their weight?

1. Is there a difference in how males and female students perceive their weight?

2. Introduction • Is there a difference in male and female body image perceptions?

3. Introduction • Data was collected on an internet-based survey from students at the University of Auckland enrolled in Stage 1 Statistics in 2009. Students received 2 marks towards their first assignment if they completed the survey. • Amongst other variables, this survey recorded students actual weight (in kgs) and their ideal weight (in kgs)

4. Problem Is there a difference in how males and female students perceive their weight? • We will look at the difference between their actual weight and their ideal weight to answer this question. Investigative question • I wonder if the medianof the difference between actual weight and ideal weight of female students enrolled in Stage 1 Statistics at the University of Auckland in 2009 tends to be greater than the medianof the difference between actual weight and ideal weight of male students enrolled in Stage 1 Statistics at the University of Auckland in 2009?

5. Investigative question Population parameter Investigative question • I wonder if the median of the difference between actual weight and ideal weight of female students enrolled in Stage 1 Statistics at the University of Auckland in 2009 tends to be greater than the median of the difference between actual weight and ideal weight of male students enrolled in Stage 1 Statistics at the University of Auckland in 2009?

6. Investigative question Population parameter Investigative question • I wonder if the median of the difference between actual weight and ideal weight of female students enrolled in Stage 1 Statistics at the University of Auckland in 2009 tends to be greater than the median of the difference between actual weight and ideal weight of male students enrolled in Stage 1 Statistics at the University of Auckland in 2009? Variable of interest

7. Investigative question Population parameter Investigative question • I wonder if the median of the difference between actual weight and ideal weight of female students enrolled in Stage 1 Statistics at the University of Auckland in 2009 tends to be greater than the median of the difference between actual weight and ideal weight of male students enrolled in Stage 1 Statistics at the University of Auckland in 2009? Variable of interest Groups/sub-populations

8. Investigative question Population parameter Investigative question • I wonder if the median of the difference between actual weight and ideal weight of female students enrolled in Stage 1 Statistics at the University of Auckland in 2009 tends to be greater than the median of the difference between actual weight and ideal weight of male students enrolled in Stage 1 Statistics at the University of Auckland in 2009? Variable of interest Groups/sub-populations Population

9. Plan • We will use a simple random sample of size 70 of the students from the stage 1 statistics students at the University of Auckland in 2009 that completed the internet-based survey. • From our SRS, we will calculate an informal confidence interval for the population median for female students and an informal confidence interval for the population median for the male students for the difference between their actual weight and ideal weight.

10. Plan That is – we’ll calculate TWO informal confidence intervals • Females • Males

11. Data • I sampled for you

12. Analysis

13. Analysis Student Task • Use the formula to construct an informal confidence interval for the population median from the samples of students • Copy the sample box plots and draw the informal confidence intervals (in red) onto the box

14. Analysis Student Task What call would we have made last year??? - Is there a difference between males and females (DIFF_Actual_Ideal) back in the population?

15. Analysis Student Task How does that transfer to our new knowledge about informal confidence intervals?

16. Conclusion – first make your inference… • From my informal confidence intervals, I am pretty sure that the population median of the difference between actual weight and ideal weight of female students enrolled in Stage 1 Statistics at the University of Auckland in 2009 is between _____ and ______ • Similarly, I am pretty sure that the population median of the difference between actual weight and ideal weight of male students enrolled in Stage 1 Statistics at the University of Auckland in 2009 is between _____ and ______

17. Conclusion – then make your call… • Based on these samples, I [would/would not] make the call that the population median of the difference between actual weight and ideal weight of female students enrolled in Stage 1 Statistics at the University of Auckland in 2009 [is/is not] greater than the population medianof the difference between actual weight and ideal weight of male students enrolled in Stage 1 Statistics at the University of Auckland in 2009 back in the population. That is, I [would/would not] make the call that the difference between actual weight and ideal weight of female students enrolled in Stage 1 Statistics at the University of Auckland tends to be larger than the difference between actual weight and ideal weight of male students enrolled in Stage 1 Statistics at the University of Auckland.

18. Conclusion Justification • The informal confidence interval for the median of the difference between actual weight and ideal weight of female students enrolled in Stage 1 Statistics at the University of Auckland in 2009 [is/is not] (much) further up the scale than the informal confidence interval for the median of the difference between actual weight and ideal weight of male students enrolled in Stage 1 Statistics at the University of Auckland in 2009 and the intervals [do/do not] overlap.

19. Conclusion • I am quite sure that if I were to take another sample of students enrolled in Stage 1 Statistics at the University of Auckland in 2009 this pattern in their difference between actual weight and ideal weight [would persist/may not persist], thus giving the same conclusion [or not…] (expand)]. • The conclusion [is/is not] consistent with my thinking that females tend to think they need to loose weight, where as males do not have such a negative body image. Further thoughts… • What would happen if to the informal confidence intervals if you increased the sample size?