4980 0 obj <>stream \nonumber\]. At the 5% level of significance, there is not enough evidence to conclude that a woman visits her doctor, on average, more than 5.8 times a year. At the 5% significance level, there is not enough evidence to conclude that the proportion of homes in Kentucky that are heated by natural gas is 0.517. However, the test is weak because the \(p\text{-value}\) and alpha are quite close, so other tests should be done. Determine the value of n. The value of n in the equation for sample mean represents how many items are being compared. Sky Ariella is a professional freelance writer, originally from New York. The Central Limit Theorem has an analogue for the population proportion \(\hat{p}\). 1 Endpoint Management Vulnerability Gap, Enterprise Strategy Group.Fieldwork was conducted in November 2022. Conclusion: There is insufficient evidence to conclude that less than 60 percent of her students feel more enriched. Cloudflare Ray ID: 7a13f2fc792f9bc2 Here are formulas for their values. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. However, the standard deviation of that age remains constant of around 2.1 years. Claims databases collect information on millions of doctors appointments, bills, insurance information, and other patient-provider communications. When the sample size is large the sample proportion is normally distributed. The mean of a sample distribution will, necessarily, be the same as the mean of the original distribution. Type I error: We conclude that the mean is not 34 years, when it really is 34 years. A broker wanted to determine if this survey could be valid. A random sample of 10 weeks had a mean number of 17.7 infections. A poll done for Newsweek found that 13% of Americans have seen or sensed the presence of an angel. The good thing about claims data is that, like other medical records, they come . A study was done to test the claim that the mean cost of a daily newspaper is $1.00. What does CLAM mean? which lies wholly within the interval \([0,1]\), so it is safe to assume that \(\hat{p}\) is approximately normally distributed. Type I error: We conclude that fewer than 5% of adults ride the bus to work in Los Angeles, when the percentage that do is really 5% or more. The first step of finding a sample mean asks us to add all the values in the sample together. ), "William Shakespeare: The Tragedy of Hamlet, Prince of Denmark," by Jacqueline Ghodsi, Scene: The great library of the castle, in which Hamlet does his lessons, (The day is fair, but the face of Hamlet is clouded. What does CLAM mean? Can you believe it? One day, as I sat down to determine the meaning of life, I got a serious craving for this, oh, so important, food of my life. The mean cost could be $1. Viewed as a random variable it will be written \(\hat{P}\). He surveyed a random sample of 250 families and found that 142 owned some type of stock. Should the personnel team believe that the mean number is ten? 6 0 obj You randomly survey 64 of her past Elementary Statistics students and find that 34 feel more enriched as a result of her class. x+TT(TH-JN-()MQ( Our body can use them more efficiently than the omega-3 (ALA) in nuts and seeds ( 6 ). Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. Type I error: We conclude that the average tuition cost at private universities is more than $20,000, though in reality it is at most $20,000. This holds true for samples of independent random variables, regardless of the population distribution, as long as the populations standard deviation isnt infinite. Be the first to rate this post. 73 2) At an urban hospital the weights of newborn babies are normally distributed, with a mean of 7.2 pounds . What is the mean number of clams per sample? The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. 20,000+18,000+20,400+21,050+23,000+22,300 = 124,750. (82-85.89) (88-85.89) (83-85.89) (89-85.89) (91-85.89) (79-85.89) (85-85.89) (93-85.89) (83-85.89) = (-3.89, 2.11, -2.89, 3.11, 5.11, -6.89, -0.89, 7.11, -2.89), (-3.89, 2.11, -2.89, 3.11, 5.11, -6.89, -0.89, 7.11, -2.89) = (15.13, 4.45, 8.35, 9.67, 26.11, 47.47, 0.79, 50.55, 8.35). Suppose you dont believe the reported figures of the percent of girls born in China. At the \(\alpha = 0.10\) level, is the Austin, TX commute significantly less than the mean commute time for the 15 largest US cities? The null and alternative hypotheses are: State the Type I and Type II errors in complete sentences given the following statements. Come Horatio, let us go together, for this is not our test. The sample mean is defined as the average of a given sample set. Use \(\alpha = 0.01\) level of significance. Does it appear that the mean work week has increased for women at the 5% level? (627,264)+(7,795,264)+(153,664)+(66,564)+(4,112,784)+(1,763,584) = 14,519,124. it is appropriate to use the normal distribution to compute probabilities related to the sample proportion \(\hat{P}\). is not four. Use a significance level of 0.05 and using appropriate statistical evidence, conduct a hypothesis test and state the conclusions. Complete the equation like you normally would to arrive at the variance of the sample. hb```a`` c B@Q>O To conclude the drug is safe when in, fact, it is unsafe. When calculating the sample mean using the formula, you will plug in the values for each of the symbols. Reason for decision: The \(p\text{-value}\) is greater than 0.01. A thin ring usually indicates a rough period of development such as lack of water, forest fires, or insect infestation. Approximately how many clams would be developing in 10 degree Celsius water? For the online version of the book, it is suggested that you copy the .doc or the .pdf files. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin? A battery manufacturer claims that the lifetime of a certain battery has a . \((0.3829, 0.6171)\). Europeans have a mean paid vacation each year of six weeks. Water temperatur. hbbd```b`` 6d_fKa "Y'[`4LIZzg 2-=DH_@o5&F3`001?; Use the information in the data table below in order to create a proper scientific graph and to answer the corresponding questions, Water Temperature (9) Number of Developing Clams 15 72 20 92 25 120 30 140 . The phone company records the following values for each of the six months: Add values together. 72 CLAMS Meaning. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. We would need to expand our sample base to include these possibilities if we wanted to generalize this claim to the entire nation. Use the Lap time data for Lap 4 (see [link]) to test the claim that Terri finishes Lap 4, on average, in less than 129 seconds. The mean for 25 randomly selected commuters is 22.1 minutes with a standard deviation of 5.3 minutes. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). \(H_{0}: p = 0.517\) \(H_{0}: p \neq 0.517\). by Nedda Misherghi and Rachelle Hall. Do not use all the data. \(H_{0}: \mu \leq 5.8\) \(H_{a}: \mu > 5.8\). Test to see if the proportion has dropped for this generation. 8600 Rockville Pike At the 5% level of significance, there is enough evidence to conclude that 48.8% of families own stocks. (20,000-20,792) (18,000-20,792) (20,400-20,792) (21,050-20,792) (23,000-29,792) (22,300-20,792) = (-792, -2,792, -392, 258, 2,028, 1,328). At the \(\alpha = 0.05\) level can it be concluded that the sample mean is higher than 5.8 visits per year? Data entry and IT jobs use sample mean values to accomplish daily goals. Parents would name their daughters with ko attaching to other Chinese characters which have meanings that they want their daughters to become, such as Sachikohappy child, Yoshikoa good child, Yasukoa healthy child, and so on. Meet Mrs. Weber A survey of 40 smokers of this generation was done to see if the mean starting age is at least 19. Ironically, I work for a company that sells products with known problems. Type II error: We conclude that the duration of paid vacations each year for Europeans is six weeks when, in fact, it is not. You catch 12 brown trout. x = ( xi ) / n. Here, x represents the sample mean, tells us to add, xi refers to all the X-values and n stands for the number of items in the data set. The student academic groups claim appears to be correct. Not to conclude the drug is safe when, in fact, it is safe. To conclude the drug is safe when, in fact, it is safe. (b) What is the independent variable? The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. A. other primary consumers \(H_{a}\), in terms of the appropriate parameter \((\mu \text{or} p)\). The sample mean is equal to the population mean. For some reason that she can't quite figure out, most people don't believe her. While the variance is a significant value to know on its own, the primary purpose of doing this equation is to be able to complete the process for determining the standard error of the set later. endstream Reason for decision: The \(p\text{-value}\)e is less than 0.05. If it does turn out that this mouth-watering dish is at most $1, then I'll throw a big cheesy party in our next statistics lab, with enough macaroni and cheese for just me. In complete sentences, also give three reasons why the two polls might give different results. Second, it is reasonable to assume that homes in the extreme north and south will have extreme high usage and low usage, respectively. Conduct a hypothesis test. This is beyond the scope of this course. We are 95% confident that between 38.29% and 61.71% of family members will shed tears at a family reunion. what is the mean number of clams per sample. Reason for decision: The \(p\text{-value}\) is less than 0.05. Type II error: We conclude that 5% or more adults ride the bus to work in Los Angeles when, in fact, fewer that 5% do. It has a mean \(_{\hat{P}}\) and a standard deviation \(_{\hat{P}}\). Let \(P =\) the proportion of students who feel more enriched as a result of taking Elementary Statistics. endstream endobj 4926 0 obj <>/Metadata 101 0 R/Pages 4923 0 R/StructTreeRoot 109 0 R/Type/Catalog>> endobj 4927 0 obj <>/MediaBox[0 0 612 792]/Parent 4923 0 R/Resources<>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI]/XObject<>>>/Rotate 0/StructParents 0/Tabs/S/Type/Page>> endobj 4928 0 obj <>stream 7 0 obj We reviewed their content and use your feedback to keep the quality high. What is the mean number of clams per sample? This table was generated using data from the CMS Chronic Conditions Public Use Files, a source of claims data.1. You dont have to be a statistician to benefit from the use of sample means. Chesapeake Lighthouse and Aircraft Measurements for . table below in order to create a proper scientific graph and to answer the corresponding questions. << /Length 8 0 R /Type /XObject /Subtype /Image /Width 2309 /Height 1844 /Interpolate Little is more crucial to the growth and success of a business than their statistical analysis efforts. [Z( %H49WA3P%h@ } The mean weaning age was nine months (3/4 year) with a standard deviation of 4 months. The organization thinks that, currently, the mean is higher. While this may not seem much better, I think that I can convince the management to use my test program instead of the original test program. Polonius enters and places some books upon the table just a moment before Horatio enters.). (c) What is the optimum temperature for clam development? The sample mean was 4.75 hours with a sample standard deviation of 2.0. While you may vaguely recall sample mean as a distant memory from high school mathematics, its applied across many fields and can be exponentially useful for many reasons. Mathematics of any kind can be initially stressful to many people, but calculating a sample mean is one of the most straightforward calculations youll find in statistics. You can specify conditions of storing and accessing cookies in your browser. Type II error: We conclude that the proportion of Americans who prefer to live away from cities is half when, in fact, it is not half. So my favorite and main staple food is macaroni and cheese. Confidence Interval: \((0.245, 0.515)\): The plus-4s confidence interval is \((0.259, 0.519)\). Book: Introductory Statistics (Shafer and Zhang), { "6.01:_The_Mean_and_Standard_Deviation_of_the_Sample_Mean" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.
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