Learn by DoingIn this activity you will learn to use StatCrunch to perform a two-sample t-test.Some features of this activity may not work well on a cell phone or tablet. We highly recommend that you complete this activity on a computer.Here are the directions and grading rubric for the discussion board exercises. A list of StatCrunch directions is provided at the bottom of this page.ContextDo undergraduates sleep less than graduate students?A student conducted a study of sleep habits at a large state university. His hypothesis is that undergraduates will party more and sleep less than graduate students. He surveyed random samples of 75 undergraduate students and 50 graduate students. Subjects reported the hours they sleep in a typical night.For this hypothesis test, he defined the population means as follows: μ 1 is the mean number of hours undergraduate students sleep in a typical night. μ 2 is the mean number of hours graduate students sleep in a typical night.VariablesHours: typical number of hours a student sleeps each night Program: undergraduate or graduate Program is the explanatory variable, and the data is categorical. Hours is the response variable, and the data is quantitative.DataTwo sample T hypothesis test:μ1 : Mean of undergraduateμ2 : Mean of graduateμ1 - μ2 : Difference between two meansH0 : μ1 - μ2 = 0HA : μ1 - μ2 < 0(without pooled variances)Hypothesis test results: DifferenceSample Diff.Std. Err.DFT-StatP-value μ1 - μ2-0.233333330.18963708106.32776-1.23042040.1106 PromptState the null and alternative hypotheses. Include a clear description of the populations and the variable.Explain why we can safely use the two-sample T-test in this case.Use StatCrunch to carry out the test. Copy and paste the content of in the StatCrunch output window (text and the table) in your initial post. State a conclusion in the context of this problem.ANSWER(S): (hint)Since we want to check whether the data supports the claim that undergraduate students sleep less, on average, than graduate students, we are testing: H 0 : μ 1 − μ 2 = 0 H a : μ 1 − μ 2 < 0 We can safely use the two-sample T-test in this case since: Both samples are random, and therefore independent.The sample sizes (75 and 50) are quite large, and therefore we can proceed regardless of whether the populations are normal or not. T = -1.23; P-value = 0.111Here is the StatCrunch output depicting these values.Two sample T hypothesis test: μ 1 : Mean of undergraduate μ 2 : Mean of graduate H 0 : μ 1 − μ 2 = 0 H a : μ 1 − μ 2 < 0 (without pooled variances) Hypothesis test results: Difference Sample Diff. Sd. Err. DF T-Stat P-Value μ1 - μ2 -0.23333333 0.18963708 106.32776 -1.2304204 0.1106 The P-value (0.111) is greater than 0.05. This indicates that the observed data is not unusual if undergraduate and graduate students, on average, have the same mean for sleep hours. Therefore, the data do not provide evidence to reject H 0 . So we cannot conclude that undergraduate students sleep less, on average, than graduate students.

First, select a social problem to analyze throughout this course. You may select from the list or come up with a social problem you wish to analyze: EuthanasiaIlliteracyHuman TraffickingAlcohol abuseInequity in the workplace Drug AbusePovertyChild AbuseJuvenile DelinquencyEconomic inequality Remember, you will use your selected social problem to complete other assignments throughout this course.In an essay format, cite one scholarly source from the GCU library in addition to the textbook and complete the following:Describe your selected social problem in its social context. (55- 75words).Use your sociological imagination to explain how the selected social problem is influenced by society (75-100 words).Select the theoretical perspective(s) (functionalist, conflict, and interactionist) that best aligns with the social problem you’ve selected to analyze in this course.Explain why the theoretical perspective(s) you chose is best to explain the selected social problem.Next, use that theoretical perspective(s) to explain how your selected social problem came to be and how it is perpetuated. (150-200 words)

The first, a hypothesis test involving a single mean, is exemplified by another question about sardines. (There are not many exciting examples that illustrate this type of test.). The second type of hypothesis test is much more interesting and it involves the difference between two means (we call this a "difference in means" test.). You have been calculating differences in means using the health survey data; in this quiz, you will carry out a difference-in-means test using data on bicycle trip duration.*** Note: All the questions, except the last one, are answerable using pen and paper. Indeed, you will come away from this class with a much better understanding of the concepts if you try to work through them "by hand" rather than first going to the computer or calculator. Thus, in addition to answering the quiz, you are required to send to me your written answers. You may scan you answers and email to me a pdf or type up your answers in Word and email it to me. You must turn in individual, NOT group, writeups, and cases of clear copying will be considered cheating and given a final score of 0.1. True or False. In statistics, the result that in large enough samples, the mean of a random variableis normally distributed, regardless of how the random variable is distributed, is called the CentralLimit Theorem2.You observe five random numbers: 2,2,3,4,4. The mean of this data is 3. What is the standard deviation? (This should be done with a pen and paper, and the formula on p. 36, note 16 of(1,3,2,0.5)3.For a random variable with the mean and standard deviation you found in Question 2 above, what is standard deviation of the sample average in repeated samples where n=5? (In other words, what is the standard error of the sample mean when n=5?). Hints: To calculate the standard error, use the formula given in equation 1.6 of Mastering Metrics. The square root of 5 is 2.25.8/9 1 2 2/9 4/94. On a can of sardines it is written that the can contains 10 sardines. You open up 100 cans andfind the average is 9.75 sardines with a standard deviation of 1. What is the test statistic in a testof the null hypothesis that the population average is 10? Can you reject the null at the 5%significance level?-2.5; no -2.5; yes -.25; no-.25; yes5.The table below contains the raw data from Professor Rietz’s six bike trips between the trainstation and the MLK library. In addition to the date of the trip and the duration, it also tells thestarting location and the ending location. Time is in minutes, rounded to the nearest wholenumber. As you can infer, Prof. Rietz arrives at the train station at the start of the day, bikes tocampus, works on campus, and then bikes back to the station at the end of the day.The average duration of trips starting at the Train Station was ___ while the average duration oftrips starting at the Library was ___6; 1010; 69; 77; 96.Consider a test of the null hypothesis that there is no difference between the average duration oftrips that start at the Library and trips that start at the Train Station. Which of the following is theapproximate value of the appropriate test statistic for such a test? (Hint: use the test statisticformula in the middle of page 45 of MM; for the standard error that appears in the denominatorof the test statistic formula, use the separate-variance formula that appears in footnote 17.)3.81.22.44.23.77.True or False: Given the value of the test statistic you found above, is the effect of starting location on trip duration statistically significant?T/F