UPP085 Academic Numeracy

Here is an excerpt from an article called “Smiles Predict Marriage Success” (by Clara Moskowitz 14/4/2009) Psychologists have found that how much people smile in old photographs can predict their later success in marriage.In one test, the researchers looked at people's college yearbook photos, and rated their smile intensity from 1 to 10. None of the people who fell within the top 10 percent of smile strength had divorced, while within the bottom 10 percent of smilers, almost one in four had had a marriage that ended, the researchers say. (Scoring was based on the stretch in two muscles: one that pulls up on the mouth, and one that creates wrinkles around the eyes.)

In a second test, the research team asked people over age 65 to provide photos from their childhood (the average age in the pictures was 10 years old). The researchers scored each person's smile, and found that only 11 percent of the biggest smilers had been divorced, while 31 percent of the frowners had experienced a broken marriage.The findings are notable because they found a connection between photos taken when people were young and marriage outcomes that sometimes occurred much later. "It feeds into this idea that what's occurring earlier in our lives in terms of our present situation and our mental state can predict things that occur decades later," said study leader Matthew Hertenstein, a psychologist at DePauw University in Indiana. "Showing the continuity in who we are is really important."

The study is detailed in the April 5 issue of the journal Motivation and Emotion.
a) What kind of study was this - observational or experimental
b) The article describes two “tests” or research studies. Identify the four steps of the research described in the first research study. 
c) What might this research be used for
d) Do the results of this study suggest that smiling for photos as a youth causes one’s marriage to succeed Explain your answer. (Big Hint: Are there other plausible explanations for the correlation.

In the second test, the participants are described as follows:
Sixty-one people from a small, Midwestern town responded to the invitation to participate in a photo study. Six individuals were removed from the sample due to their photos not being clear enough to code. The remaining sample consisted of 55 mature adults (44 female and 11 male). Participants were asked to provide up to eight photographs of themselves between the ages of 5- and 22-years-old.
e) What is the sample in the second test How was it selected Are there any problems with this sample and how the data was collected Explain your answer. 
f) Thinking about the research as a whole, critically evaluate the research by writing a paragraph that summarises the good and bad points of the research.

1. The given study is observational and not experimental as the researcher is just observing and collecting the available data and also cannot manipulate data which is possible in an experimental study.
2. The four steps in the first research study are as follows.

• State the hypothesis (Null and Alternative)
• Determine the level of significance and also the test to be deployed.
• Perform the test and compute the test statistics along with either the critical value or p value.
• Based on the value obtained for the t-statistic and the corresponding p value or critical value, a conclusion is reached whereby either the null hypothesis would be rejected or not rejected.

1. This research is used to establish whether the two given variables are independent or dependent.
2. I think in this particular study there could be certain confounding variables which can impact the relation between the two variables and thus reduce the overall validity and reliability of the conclusion drawn in the studies. It is quite possible the difference may be attributed to social factors, cultural factors, legal factors which are equally important for the divorce rate. For instance, amongst the Asians, the divorce rate are much lower than the West which is attributed to cultural and social reasons. Also, family support could be a crucial aspect which cannot be ignored.
3. The sample consists of 61 individuals that are selected from a town through invitation. The sampling in the given case in not random as anyone who wants to attend is invited with the only caveat being that requisite number of photos must be available. Yes there are issues with the sample as this would not be representative of the population and would be biased. This is because it is highly likely that those people would come forward who are good looking and hence would tend to have attractive smiles. Further, in case the respondents are aware of the exact relation that the researchers wish to seek, then it is highly likely that people who are not divorced would participate.  Also, the data is way too skewed with regards to gender since females are four time the number of males which cannot be representative of any population.
4. One good point about the given research include an attempt to base the data based on quantitative data rather than relying on qualitative data. Another good point is that fact that the given research has relied on primary data rather than relying on secondary data. However, a big drawback of the study is the inability to account for the various confounding variables which could potentially be impacting the validity of the results obtained. Also, another drawback of the research is the incorrect sampling technique used as a result of which the sample obtained would be biased towards a particular conclusion hampering the reliability and validity of the study.
5. Sample mean = Total sum of all the 16 houses/ Number of observations = 5087000/16 = $ 317,937.5
6. The mode of the given sample data Is $ 220,000 since it has the highest frequency of 2 in he given data.
7. The median value is the average value of the 8^thand 9^th value when arranged in ascending or descending order = (280000 + 300000)/2 = $ 290,000
8. Range of the sample = Maximum value – Minimum Value = 935000-176000 = $759,000
9. The stacked dot plot is indicated below.
10. The mean, median, mode are indicated in the dotplot below.
11. The real estate agency has used the median price. Based on the given distribution which seems to be skewed on the right which is distorting the mean value, the median value seems to be an appropriate measure.
12. Looking at the given scatter plot and the value of the correlation related to the line of fit, it seems apparent that there does not seem to be a causal relationship between the time of eating food and obesity rates. This is confirmed as the line of best fit is sloping downwards but the deviation of the points from the line seems very high. Also, the magnitude of correlation coefficient can be used to determine R²or coefficient of determination which would be equal to (0.18)² = 0.0324. This indicates that only 3.24% change in the obesity rates is explained on account of changes in the time spent on eating food.
13. Four possible explanations for the value of correlation observed are outlined below.

• The speed of consuming food tends to impact the actual food intake hence fast eaters tend to consumer more food.
• There are other factors which are important in determining the obesity rate and hence the correlation is low between the two variables.
• Higher time on eating food may result in higher intake of food leading to higher consumption of food.
• Higher time on eating food also suggests that lesser time is spent on other activities which may help in burning calories and thus the correlation.

1. It is apparent that there are other factors which are responsible for the pattern observed. One of these would be nature of food that is eaten particularly with regards to calorie contents. The food habits tend to differ in various nations and typically the nations which have a higher incidence of fast food and junk food consumption tend to show higher incidence of obesity. Another relevant factor is the lifestyle which is sedentary would lead to obesity and if not, then the calories intake would be used and obesity rates would be lower. Additionally, the genetic factors are also important in certain cases coupled with the socio-cultural factors as in certain culture, obese people may be less acceptable socially while in others, the acceptability may be higher.
2. The inference drawn that aged 16-19 are safe against people in the 20’s would be wrong to infer based on the given data as it lists down the number of drivers involved in fatal crashes. However, to conclude about the safety, the total number of drivers in each of the age group must also be considered and the proportion should be derived. For instance, it is but obvious that number of people who are driving in their 20’s would be significantly higher than age 16-19 and hence it is likely that since the age 20’s represent a higher percentage of the population of drivers, hence they account for higher fatal accidents as well.. Similarly, the number of octogenarians who may be driving would be significantly lower than other age groups and thus the fatalities are lesser. In order to measure the safety, it is pivotal that proportion of drivers in each age group involved in fatal accidents need to be recoded which would allow comparison in this regard.

(b) The age group 20-24 would represent the mode of drivers involved in fatal car crashes.

1. c) The given graph is not normal as there is presence of positive skew or rightward skew which is apparent from the long tail of the curve stretching on the right side. This implies that there is higher distribution of values at the extreme right which would distort the mean value and as a result the median value would be lower than the corresponding mean value. The mean and median in the given case would both lie in the interval 25-29.
2. d) Considering that the data is positive skewed, hence median would be appropriate measure of average for the situation provided.
3. Two variables having a positive correlation would be the number of junk foods meals eaten each week and the body mass index.
4. Two variables having a negative correlation would be minutes spent exercising each week and the body mass index.
5. Two variables with no correlation would be the number of siblings the students have and the average number of pets a student has.
6. A student who would tend to spend more time doing exercise would more likely be fit and would tend to be less obese on account of the calories and excess fat burnt during the exercise. As a result, the BMI or Body Mass Index for the concerned student would be lesser.
7. This graph is about the relationship between the weekend temperature and the number of beach balls sold.
8. The scale on the X axis should be arranged in ascending order i.e. starting from a lower value of temperature and increasing the value as one moves to the right. This would enable the reader to draw useful inferences about how temperature tends to impact the sales of beach balls. Additionally, the colors used to represent the various bars should also be the same as different bars tend to indicate some differences which do not exist in this case. Also on the X axis, the appropriate unit for temperature should also be mentioned.