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A sample is considered as taking into account the whole population is impossible. For example, if I want to calculate the average height woman in a country. It is highly impossible to collect the data from all the women in the country. So I collect 10,000 woman at random and perform relevant statistics and conclude from the sample about the population data. For better inference, considering more than one sample is a common practice.
A statistical inference is done based on the laws of probability, sampling allows analysts to draw conclusions based on parameter statistics(sample mean, sample varianc, etc. ) performed on sample data regarding the population data. A random sample is crucial as the distrbution will be skewed if the sample drawn is not random.
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- Part 1: Consider sampling in statistics. Why do we take samples? Why do we want representative samples (and what does it mean)? Part 2: Are there limitations to the data source and your sample (For example, my data and sample is about animals)? Why? How might you design this differently to get a more representative sample? Further - in your opinion is there still value to be gained even if a sample is not representative?arrow_forwardA researcher conducts a study to investigate whether the obesity rate rural communities differ from the obesity rate from the population at large. He gathered a sample of adults from a small community, measured their weight, and compared it to the population average. What statistical test is appropriate for this study and why?arrow_forwardHi could you fill out the blanks?arrow_forward
- Do you think that by choosing the statistical analysis first, and then deciding upon what kind of research plan (i.e., so that the data will suit the analysis) could bias the entire research enterprise?arrow_forwardAccording to previous studies, 12% of the U.S. population is left-handed. Not knowing this, a high school student claims that the percentage of left-handed people in the U.S. is 14%. The student is going to take a random sample of 1650 people in the U.S. to try to gather evidence to support the claim. Let p be the proportion of left-handed people in the sample. Answer the following. (If necessary, consult a list of formulas.) ✔ (a) Find the mean of p. P. 0 (b) Find the standard deviation of p. (c) Compute an approximation for P (P<0.14), which is the probability that there will be 14% or fewer left-handed people in the sample. Round your answer to four decimal places. Xarrow_forwardA) We have just conducted a study examining how much math anxiety students experience after taking a statistics class. We want to know if students on average are reporting low (1) or high (7) levels of math anxiety. To do that, we want to compare the math anxiety levels of the students after they have taken a statistics course to the average population math anxiety. We believe that the students on average will have a level of math anxiety that differs from the population. X 3 4 4 5 5 3 1 3 5 6 7 2 2 3 2 3 2 3 1 3 Report our null and alternative hypotheses in words. Given the information we have, what specific t-test do we need to run in order to examine our hypothesis? Provided are the ratings from the students that we recruited (see left), the mean and standard deviation for that sample (see below), and the population average (see below): xbar =3.35, Meu=4.00 and SD=1.60…arrow_forward
- It's important to understand that hypothesis testing is just how statisticians (by "statisticians" I mean people who are working with data, e.g. analysts, auditors, economists, whoever) answer quanitative questions. We intuitively know that not much is truly certain, and that it's really hard (if not impossible) to collect data on everything we are curious about. So we use samples and try to extrapolate to a larger population. For this discussion, I would like each of you to come up with your own interesting hypothesis test. So, you will do the following: 1) Explain the context or story for which you have a problem stats might be able to help with. 2) Come up with the null and alternative hypotheses. This can be in words, or numbers, or a combination of both (I'll give an example below). 3) Explain where/how you might collect data to reach a conclusion for the test. 4) (RESPONSE) When you respond to someone else's post, I want you to critique their test and data. If you can, suggest a…arrow_forwardWhat is the Sample?arrow_forward
- A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
