MAT-274 DQ\'s PDF

Preview

Summary

Discussion Questions...

Description

TOPIC 1 DQ1 Excel itself is a useful tool that can be beneficial in many aspects of a person's life because of the ease of use that it provides when it comes to inputting data and information. I am majoring in Biology with an emphasis in Pre-Medicine and the way that I plan to be able to use Excel to my advantage is mainly in terms of the many math and science courses that I am required to complete for my major. I expect that I will have to chart and graph data during experiments and Excel seems to be the best option when it comes to tracking data. I also think that Excel will benefit me in that it will make it easier for me to create a weekly schedule and therefore to keep better track of my time. Another way that I believe Excel can be beneficial is when it comes to reviewing data. Excel makes it easy to organize and go over data, especially when it comes to sharing the information with peers. DQ 1 RESPONSE 1 Hi Jeanette, Your future career choice sounds like a very demanding, but very fulfilling option. Pediatric nurses are amazing and, as you said, they do lots of charting and recording of information which would be a perfect reason to use Excel. Excel is not only great for keeping track of information, it is also great for easily accessing and sharing the information quickly and easily. DQ1 RESPONSE 2 Hi Hunter, I think that the equation solving aspect of Excel is pretty fantastic as well! In my MAT-261 I created my own equations for interest and payment plans because I tried to do my projects before my professor explained how to do it an easier way. My mistake actually ended up being very beneficial to me in the long run because it helped me to understand how to use Excel faster since I navigated it on my own. DQ2 The mean and median are useful when it comes to different types of data because they are not the same tools. The mean is something used to find averages; it is used when attempting to find what is considered a standard number or amount in terms of a particular table of terms. An example of this could be when looking at vehicles and comparing prices. If a person took a list of different prices from different companies for the same car, added them together, and then divided that number by the number of terms, he/she could find the average price of the vehicle, and therefore, shop in that range. A median is quite different from a mean. The median is considered the centermost number in a list of terms. This is found by splitting a term list in half and finding what the number is that has

half of the terms in the list above the number and half of the terms in the list below the number. This should be used when there is an outlier in a data table. For example, when looking at a list of average jean prices: 15,17,20,27,29,30 and 64, there is an outlier (a number that is not close to any of the other numbers, that would skew the average and make it higher than the middle term), 64, then the centermost number, or median, 27 should be considered the best option as the closest number to an average without such a large number to change the mean so drastically. DQ2 RESPONSE 2 Hi Carolina, I like your use of the term outliers in describing when not to use mean. That is a key point in the difference between median and mean. Also, your choice to use the example of student test score percentages for both the median and the mean was very helpful to explain the slight difference without using two different examples. DQ3 To understand the similarity between the standard deviation and the z score of a distribution, you must first understand what each term means. Standard deviation is, to be quick, the measure of the distance between the mean, which was found based on a set of data, and any given point in a set of data. To find the standard deviation, one must first start by finding the mean of a given data set and then calculating the variance. After calculating the variance, one must find the square root of it which should be the standard deviation. The standard deviation is the average distance between any point in a data set and the calculated mean. This is usually shown in the form of a bell curve. The Z score is essentially the number of times that the standard deviation is used to get to any particular point. For example, if the mean of a data set was 2 and a given point on the data set was 4 but the standard deviation was 1, then the point given (4) is considered two standard deviations away from the mean, therefore, the z score was 2 standard deviations. DQ 3 RESPONSE Hi Meghan, I appreciate that you talked about drawing a graph to help understand the concept. So many people are visual learners and I feel like understanding the bell-shaped-curve is really an essential part of understanding the concept. Also, the source you cited had some good clarifying information on it. Good job! DQ 4 When choosing a home, there are many things that have to be taken into consideration. Of the most important are the typical number of bathrooms and bedrooms, the square footage, and the appraised value of houses in the neighborhood. For each factor there is a different way to choose the best central tendency. For the average number of bedrooms and bathrooms the mean would be the most suitable choice as the goal is to find the typical number of bedrooms and bathrooms

in houses in a certain neighborhood. When it comes to the square footage, however, utilizing the central tendency, median, would be the best option as it eliminates the outliers and is still a centralized value. Lastly, the centermost appraisal value can also be best found using median since it rids the outliers. Another example of something where central tendency can be used is the average water bill over the course of a year. The mean would be the best option for this since the water bills would need to be averaged over the course of the year. DQ 4 RESPONSE Hi Alycia, I think you are correct in suggesting that the median value of the houses in the neighborhood would be the best option as there are always some random overpriced houses on the market. I also think that choosing the mode for the number of bedrooms and bathrooms was a good option because of the fact that majority of houses generally have a consistent number when it comes to neighborhoods, but I do think that the mean could be used here as well. The mean would be a good option for square footage. Good job. TOPIC 2 DQ 1 Suppose you wanted to select a representative random sample of students on your campus for a face-to-face interview. How would you ensure that your sample was random as well as representative of the student population? A sample, in terms of statistics and sample surveys, is a group of people selected from a population of individuals, which is always a larger group. When taking a sample survey of students on your campus for a face-to-face interview there are many requirements for ensuring that the sample is random. They are being gender-inclusive and to ensure that both genders are represented, to make sure that students of every grade level are represented, to make sure that a multitude of majors are represented and maybe even to make sure that students from all different parts of campus and during different times of day are interviewed. This way, opinions are taken from students of every different background and a multitude of different, unbiased factors are included. On another note, one must also keep in mind the number of students on campus and take a hefty percentage of the population to be considered an adequate sampling. DQ 1 RESPONSE Hi Savannah, A sample is a group of people selected from a certain population to participate in some time of survey or experiment. I felt that you did a good job listing factors that should be taken into

consideration when it comes to making sure that the sample group in question is indeed randomized. DQ2 There is one key difference in distinguishing an observational study from an experimental one. In both studies observations are made and the conclusion of the study is dependent on these observations, but that is the only aspect of observational studies. Observational studies consist of simply taking down information and data while experimental studies have an added aspect; these studies require that something must be changed within the experiment parameters and the data recorded must come from the experiment before any variable(s) were added and after the variable(s) were added. An example of each of these studies would be: Observational Study: Recording the information gathered after noting the number of cars of each color in the parking garage at a particular time of day. Experimental Study: Giving one group of college aged students an energy drink and giving another group of students only water and recording their respective heart rate changes and similarities throughout the day. DQ2 RESPONSE Hi Madelyn, I felt that your Discussion Question response was interestingly formatted and I appreciated that you pointed out the correlation that observational studies and experimental studies have in terms of statistics. Explaining your examples in terms of each other instead of using two different examples was also a good choice and I feel like that definitely made the differences easier to understand. Good job. TOPIC 3 DQ1 I chose an article that studied the correlation between nausea and vomiting during pregnancy and sex outcome of the fetus using inferential statistics. The authors interviewed postnatal mothers and asked them questions about their medical history regarding nausea and vomiting. The authors prompted questions about nausea frequency/duration during pregnancy, the weeks in which the feelings were most common, the associated symptoms and if any medication was taken to alleviate the feelings of nausea (NAYAK, 2017). The authors then compared the pregnancies with the most nausea/vomiting reported with the sex of the newborns. According to previous studies there is a slight association between the hormones of female fetuses and maternal nausea and this study verified that association and said that there is a p-value of 0.011 and a relationship at a 5% level of significant (NAYAK, 2017). The authors used Fisher's Exact

Test and the Chi Square Test, which were computed between morning sickness and the gender of the newborn, to identify any correlation between the two variables (NAYAK, 2017). NAYAK, S., & B., S. (2017). RELATIONSHIP BETWEEN MORNING SICKNESS DURING PREGNANCY AND INFANT GENDER AMONG POSTNATAL MOTHERS. Journal On Nursing, 7(2), 21-26. DQ1 RESPONSE Hello Ashley, I think the fact that there is a direct association with menopause and raised levels of these hormones is fascinating and not at all shocking as a lessening of hormones is part of the causation behind menopause. Overall this was a very interesting article to have chosen and you did a good job explaining the basic outline of the study while also touching on the p-value, correlation, and the type of statistical test used. Good Job.

DQ2 Binomial Probability Distribution is a type of formula used to identify the statistical probability of a particular outcome occurring out of a specific number of trials. The cases where binomial probability distribution should be used are when there are only two possible outcomes (bi means two), and the two outcomes are typically considered a success or a failure depending on the expected or chosen outcome. The binomial distribution model is typically defined by n (the number of trials), x (the number of times that the expected or chosen outcome occurs), and p (which is the probability of the successes (x) in a number of trials (n)). An example of this would be taking a group of people and asking them to say whether or not they prefer cats or dogs. Another example would be if you had a bag of marbles, half blue and half red, and asking someone to reach in and grab one. The probability would lie in whether the participant would pull out a red or a blue marble. LaMorte, W. W. (2016, July 24). The Role of Probability. Retrieved January 29, 2018, from http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Probability/BS704_Probability7.html DQ2 RESPONSE Hi Ashley, Binomial probability distribution is only used when there are only two possible outcomes the outcomes are either considered a success or a failure depending on the expected or chosen outcome. For your example you used rolling a die to see if you could land on a one. Your prediction/expected outcome is that you will land on a one, therefore every time you do so, those trials are considered successes and every time you do not, those trials are considered failures.

Because of the fact that your outcomes can only be success or failures, this is a good example of binomial probability distribution. DQ 3 In basic instances a mean is the average of a set of given data points. In terms of probability, standard deviation is the measure of the distance between the mean and any given point in a set of data. Variance though, is the average of the squared differences that were found from the mean. Probability distribution is typically a table or equation that displays the probability of the occurrence of a particular outcome. In terms of the description of a probability distribution, the mean is used to find the most probable outcome from the suggested possible outcomes. The standard deviation of the probability distribution is the square root of its variance. In terms of the possible outcomes suggested by probability distribution, the standard deviation and the variance are used to measure the average (mean) distance from the average (mean) outcomes/values. Mean, standard deviation, and variance are all intertwined in their definitions, uses, and purposes, therefore they are all required, for their own reasons to assist in describing probability distribution. DQ 3 RESPONSE Hi Mustapha, I think you chose good examples in your description of what mean, standard deviation, and variance are. Also, your references were so helpful in guiding along my understanding of the topic itself, as I was struggling to find the purpose of mean, standard deviation, and variance in terms of the probability distribution. Good Job. DQ4 The central limit theorem is a theory that, in terms of statistical probability, states that when a sample is taken of a population, if that sample is large enough and random enough, it will accurately represent the mean of the entire population despite only being a sample. This is true in terms of the fact that as the population grows, the sample size should also grow so that the accuracy of the sample’s representation will continue. An example of this would be when taking a survey of the number of people at GCU that have their cars on campus. The sample would not just come from one chosen group of students, such as students that are from Arizona because that percentage is going to be higher than the actual average due to the fact that they had less obstacles in having their cars on campus. The sample should be a large, random grouping of students so that there is no skewing of the data collected. DQ4 RESPONSE

Hi Jeanette, The central limit theorem is a theory that says that for a sample to be accurate, it must be large enough and random enough to represent the population in its entirety. It also says that as the population increases, so should the sample. I like the route you took in explaining your example and I felt that you did a good job in thinking out of the box. Nicely done. DQ5 Variables are typically just placeholders for values that are not constant or for values that have yet to be determined. The two different types are discrete and continuous random variables. The difference between these two variables lies in how they are determined.The first type, a discrete random variable, should be a variable that has a definite countable number of possible variables like the number of freckles a person has on their face. The second type, a continuous random variable, is typically a variable that is not definite and that cannot be counted to a stopping point. An example of this would be the number of people in the world. This is because the number is ever changing with deaths and births occurring every second. We can identify discrete vs continuous phenomena when collecting data by simply taking note of how we are finding what the variable represents. The variable will either have to be a fixed point or be taken at fixed intervals (discrete) or it will be essentially endless/forever changing (continuous). DQ5 RESPONSE Hello Mustapha, In the differences between variables, it is important to note that variables, technically, must always be of numeric countable value and it was great that you emphasized that point in your introducing of this topic. The difference between these two variables is simply in terms of whether the variable has a stopping point or if it is endless and you did a good job displaying the difference in your examples. Nice Work. DQ6 When flipping a coin five independent times and having X represent heads, the type of variable that X would be is called a discrete variable. A discrete random variable should be a variable that has a definite countable number of possible variables like the number of times a coin lands on heads when flipped a finite number of times. The reason that it is not a continuous random variable is that this type of variable typically a variable that is not definite and that cannot be counted to a stopping point. Sample space is the grouping of all the possible outcomes that could occur as results of an experiment/trial that is based on probability. Based on the fact that there are two sides of a coin and therefore a 50% probability for each flip of a coin to land on heads, the sample space for

flipping said coin five times with the coin landing on heads every time would be roughly 3.13%. All outcomes for flipping the coin, theoretically, are equally likely. DQ6 RESPONSE Hi Sarah, All of the results of the experiment are random and therefore you are correct in suggesting that any combination of heads or tails could occur in any part of the 5 flips during the trial. The possible outcomes could favor heads over tails or vice versa. Because the experiment is indeed random, only the possibilities can be predicted, but there is no real way of knowing the results without actually doing the experiment. Nice work. Topic 4 DQ1 The p-value of a statistical experiment is something used by researchers to find and measure the probability of the results favoring the null hypothesis. The higher the p-value, the higher the probability of disproving the null hypothesis. Researchers use the p-value to see if it follows the standard/normal distribution of a curve, which helps them to understand if it proves or disproves the null hypothesis. The null hypothesis is rejected if the p-value is less than a predetermined level. This is called the significance level, and it is the probability of rejecting the null hypothesis given that it is true If the p-value is smaller than the level of significance then it that shows that, in terms of evidence, the data is not strong enough or evident enough to support the hypothesis rather than the null hypothesis. The level of significance is typically set at 5% or below, in terms of the curve. DQ1 RESPONSE Hi Mustapha, The p-value is used in relation to the null hypothesis, in terms of experimentation. When the p-value is high, that is like saying that there is strong/evident data to support the hypothesis, but when the p-value is low (typically...