Claims databases collect information on millions of doctors' appointments, bills, insurance information, and other patient-provider communications. Water Temperature in OC , Number of developing clams 20 25 30 35 40 45 50 75 90 120 140 75 40 15 A clam farmer has been keeping records of the water temperature and the number of clams developing from fertilized eggs. Did the class demonstrate that the percentage was higher in Owensboro, KY? What symbol represents the random variable for this test? A sample of a college math class resulted in the following family sizes: 5; 4; 5; 4; 4; 3; 6; 4; 3; 3; 5; 5; 6; 3; 3; 2; 7; 4; 5; 2; 2; 2; 3; 2. The mean number of words per minute (WPM) typed by a speed typist is 72 with a variance of 100. Answer any other questions asked in the problem. Instructions: For the following ten exercises. The null and alternative hypotheses are: State the Type I and Type II errors in complete sentences given the following statements. (b) What is the independent variable? - Welcome! The distribution to be used for this test is \(\bar{X} \sim\) ________________. 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. He paces the large room. Based on the data shown, what can be concluded about the comparative health of Forest A & B? Automated acceptance testing Code Code Review Compile Safe Agile Devops Develop describes the practices necessary to, are from SAFe DevOps 5.0 Which technical practice incorporates build-time identification of security vulnerabilities in the code? Water Temperature (C) Number of Developing Clams 15 72 20 92 25 120 30 140 35 99 40 72 45 36 50 0 1. At a significance level of \(a = 0.05\), what is the correct conclusion? Let \(x =\) the number of sick days they took for the past year. 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 35 99 40 72 45 36 50 0 (a) What is the dependent variable? Reason for decision: The \(p\text{-value}\) is less than 0.05. (Hamlet resignedly attends to his task.). What is the dependent variable? A recent survey in the N.Y. Times Almanac indicated that 48.8% of families own stock. Hypothesis testing: For the following ten exercises, answer each question. To recognize that the sample proportion \(\hat{p}\) is a random variable. What does CLAMS mean as an abbreviation? To conclude the drug is safe when, in fact, it is safe. An online retailer claims that \(90\%\) of all orders are shipped within \(12\) hours of being received. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. You catch 12 brown trout. In other words, the data found at the phone company demonstrates inconsistent sample values and wont be representative of the entire phone industrys average numbers. (Some are repeats.) stream This gives a numerical population consisting entirely of zeros and ones. (Horatio and Polonius leave together. A medical investigation claims that the average number of infections per week at a hospital in Westchester is 16.3. \(p\text{-value} = 0.000002\) which is almost 0. Does it appear that the mean work week has increased for women at the 5% level? To apply this to the example of the phone company, they begin by adding together the number of customers they had each month. If the mean is 20 claims and the standard deviation is 3 claims, what is the probability that in a randomly selected month, the insurance company's claims are less than 26 claims? Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. Data (length of mean work week): 70; 45; 55; 60; 65; 55; 55; 60; 50; 55. There is insufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is at least 20%. Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. The sample mean of the test scores in the professors class is 85.89. Recently, many groups have been studying whether or not the women's movement has, in fact, resulted in an increase in the average work week for women (combining employment and at-home work). A newly hired engineer hopes that its shorter. Thus the Central Limit Theorem applies to \(\hat{p}\). This table was generated using data from the CMS Chronic Conditions Public Use Files, a source of claims data.1. There is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is less than 20%. \(H_{0}: \mu \geq 150\) \(H_{0}: \mu < 150\). The proceeding xi within the parenthesis means all x-values, which would be the values for each piece of data youre investigating. The sample standard deviation is 1.8. POLONIUS: So, Horatio, what is it thou didst reveal through thy deliberations? Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. This is so unlikely that it is reasonable to conclude that the actual value of \(p\) is less than the \(90\%\) claimed. The formula for solving the sample mean is x#772;=(xi) / n. At first glance of this formula, you may already be ready to throw in the towel, but the complicated seeming language of the equation is actually fairly easy when broken down. Cloudflare Ray ID: 7a13f2fc792f9bc2 I have a feeling that, while 70 percent or more of my mothers generation would have names with ko at the end, the proportion has dropped among my peers. It made me stop and think. The mean starting salary for San Jose State University graduates is at least $100,000 per year. The more spots, he thought, the more shekels. I've often wondered how software is released and sold to the public. She randomly surveys 56 online students and finds that the sample mean is 29.4 with a standard deviation of 2.1. Let \(\bar{X} =\) the average cost of a daily newspaper. This is beyond the scope of this course. The mean number of cars a person owns in his or her lifetime is not more than ten. 1. A fish psychologist determines the I.Q.s as follows: 5; 4; 7; 3; 6; 4; 5; 3; 6; 3; 8; 5. The sample mean was 4.75 hours with a sample standard deviation of 2.0. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Conduct a hypothesis test to see if your decision and conclusion would change if your belief were that the brown trouts mean I.Q. \(H_{0}: \mu \leq 5.8\) \(H_{a}: \mu > 5.8\). Type I error: We conclude that the mean starting salary is less than $100,000, when it really is at least $100,000. $2.02 !!! Standard error is also a measure of how the numbers are spread out among the set, but its evaluating how far each data point is from the mean as opposed to each other. << /ProcSet [ /PDF /ImageB /ImageC /ImageI ] /XObject << /Im1 7 0 R >> >> So why cant man catch brown trout? Suppose you believe that the brown trouts mean I.Q. endobj State a consequence of committing a Type II error. The mean weaning age was nine months (3/4 year) with a standard deviation of 4 months. Find the square root of the variance value. Square the resulting values. % To test if 68% also represents Californias percent for full-time faculty teaching the online classes, Long Beach City College (LBCC) in California, was randomly selected for comparison. The wave below occurred in 1 second. Threat modeling Dynamic code analysis - can not be the answer. Before attempting to solve for your organizations sample mean, you must first consider the formula. Is sample mean and mean the same? Your IP: To recognize that the sample proportion \(\hat{p}\) is a random variable. In terms of the example with the phone company, this would mean subtracting 20,792 from the value of every month. When youre only looking at a sample group, however, you use the term sample mean. The historical probability and the number of claims for each type in the current year are: Type Historical Probability Number of Claims in Current Year A 0.2744 112 B 0.3512 180 C 0.3744 138 You test the null hypothesis that the probability of each type of claim in the current year is the Login . Conclusion: There is insufficient evidence to conclude that the average IQ of brown trout is not four. Performance & security by Cloudflare. hbbd```b``
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Calculate \(\sigma_{x} =\) __________. Determine the value of n. The value of n in the equation for sample mean represents how many items are being compared. However, the standard deviation of that age remains constant of around 2.1 years. << /Type /Page /Parent 3 0 R /Resources 6 0 R /Contents 4 0 R /MediaBox [0 0 841.8898 595.2756] The concept of sample mean will arise early on in learning about statistics. Thus. If you are using a Student's \(t\)-distribution for one of the following homework problems, you may assume that the underlying population is normally distributed. Distribution of the Sample Mean and the Central Limit Theorem . Filter by: Select category from list. The best estimate of the population mean is sample mean X \bar{X} X which is 20 . A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. Claims data, also known as administrative data, are another sort of electronic record, but on a much bigger scale. In America, most nursing mothers wean their children much earlier. The information given is that \(p=0.38\), hence \(q=1-p=0.62\). What is the mean number of clams per sample? 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. First, the samples population is only the state of Kentucky. A phone provider company is interested in learning more about the statistical trends of its customer base. The mean for 25 randomly selected commuters is 22.1 minutes with a standard deviation of 5.3 minutes. Experts are tested by Chegg as specialists in their subject area. At the \(\alpha = 0.05 level\), can it be concluded that the mean rainfall was below the reported average? Suppose you dont believe the reported figures of the percent of girls born in China. If the mean is 20 claims and the standard . What is sample mean equal to? Type I error: We conclude that the proportion of Americans who prefer to live away from cities is not about half, though the actual proportion is about half. This page titled 9.E: Hypothesis Testing with One Sample (Exercises) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. Step 5: Divide the sum by one less than the number of data points in the sample. The mean of a sample distribution will, necessarily, be the same as the mean of the original distribution. Reason for decision: \(p\text{-value} < \alpha\). Let \(P =\) the proportion of students who feel more enriched as a result of taking Elementary Statistics. They head to the kitchen to set out the mats. The classes in which I napped and snored. To learn what the sampling distribution of \(\hat{p}\) is when the sample size is large. However, youve already done most of the legwork to solve for standard error once youve run these equations. Suppose that a survey is conducted to determine this years rate. Is this a test of one mean or proportion? \(H_{a}\), in terms of the appropriate parameter \((\mu \text{or} p)\). At most 60% of Americans vote in presidential elections. We would make the same conclusion if alpha was 1% because the \(p\text{-value}\) is almost 0. Based on the results that follow, should she count on the mean work week to be shorter than 60 hours? POLONIUS: My Lord, how canst thou admit that thou hast seen a ghost! I usually use the test program X, which tests the product, to try to create a specific problem. NOTE: For more accurate results, use more California community colleges and this past year's data. Following are the names. Legal. This means that most of the scores in the class fall within 4.36 points above or below the mean of 85.89. %PDF-1.3 However, I was determined to find out. 72 The alternative hypothesis is: 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.
The organization thinks that, currently, the mean is higher. Population mean} a. {qibXMdT
-LL42UR&g++Ki5V,lp. In this study, you count the number of girls and boys born in 150 randomly chosen recent births. A sample of 42 individuals at a shopping mall found that the mean number of visits to a restaurant per week was 2.98 with a standard deviation of 1.68.Find a 90% confidence interval for the mean number of restaurant visits A 90% confidence interval for the mean number of restaurant visits is (Use ascending order. 2003-2023 Chegg Inc. All rights reserved. hb```a`` c B@Q>O Nine hundred randomly selected voters are asked if they favor the bond issue. 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. _______________________________, 4. The sample mean was 18.1 with a sample standard deviation of 1.3. Use all twenty races given. How is sample mean calculated? To conclude the drug is safe when in, fact, it is unsafe. We all get together from different towns. 4980 0 obj
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What is the optimum temperature for clam development? Suppose you believe that the mean time is longer. The result is called the variance. Find the probability that the mean time spent studying per week is greater than 9.5 hours. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. One hundred grams (g), or about 3.5 ounces (oz) of canned clams from Chicken of the Sea contains a whopping 29.45 mg of . Type II error: We conclude that the mean number of cars a person owns in his or her lifetime is not more than 10 when, in fact, it is more than 10. What does CLAM mean? In basic terms, the Central Limit Theorem states that as a sample mean becomes larger, it approaches a normal distribution. \(H_{0}: \mu \geq 11.52\) \(H_{a}: \mu < 11.52\). Viewed as a random variable it will be written \(\hat{P}\). Conclusion: There is sufficient evidence to support the claim that the mean cost of daily papers is $1. At the \(\alpha = 0.05\) level can it be concluded that the sample mean is higher than 5.8 visits per year? (With Examples). (After all, as a poor starving student I can't be expected to feed our class of animals! Sky Ariella is a professional freelance writer, originally from New York. 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. We would need to expand our sample base to include these possibilities if we wanted to generalize this claim to the entire nation. 2 Gartner Press Release, Gartner Survey Shows 75% of Organizations Are Pursuing Security Vendor Consolidation in 2022, Gartner.September 13, 2022. From Longman Dictionary of Contemporary English clam1 /klm/ noun [ countable] 1 a shellfish you can eat that has a shell in two parts that open up clam chowder (=a type of soup) 2 as happy as a clam 3 American English informal someone who does not say what they are thinking or feeling Examples from the Corpus clam She wrapped . Assume the amount of summer rainfall follows a normal distribution. So I went down the street to Greatway to get a box of macaroni and cheese, but it was SO expensive! Advertisement. The mean work week for engineers in a start-up company is believed to be about 60 hours. ___________________________________________________, 2. I wrote down all my Japanese friends, ex-classmates, co-workers, and acquaintances names that I could remember. Research Brief #3. State the null hypothesis, \(H_{0}\), and the alternative hypothesis. What is the probability that the sample mean would differ from the population mean by more than 3.3 WPM if 43 speed typists are randomly selected? Members of a personnel department do not believe this figure. Accessibility HAMLET, Prince of Denmark and student of Statistics, HOROTIO, friend to Hamlet and fellow student, Let \(P =\) the proportion of errors generated. Thus the population proportion \(p\) is the same as the mean \(\) of the corresponding population of zeros and ones. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. %PDF-1.5
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to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher, to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same, to conclude that the mean hours per week currently is 4.5, when in fact, it is higher, to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher, \(N\left(7.24, \frac{1.93}{\sqrt{22}}\right)\). Conclusion: There is sufficient evidence to support the claim that less than 50% of his friends have pierced ears. It conducts its own survey. State the distribution to use for the hypothesis test. However, the test is weak because the \(p\text{-value}\) and alpha are quite close, so other tests should be done. Thirty randomly selected fatal accidents are examined, and it is determined that 14 were caused by driver error. You decide to check this out on your own. CLAMS. Every business cares about predicting trends for a larger population based on a smaller sample size. The good thing about claims data is that, like other medical records, they come directly from notes made by the health care provider, and the information is recorded at the time patient sees the doctor. HAMLET: That you must teach me. For that same year, a survey was conducted of 41 California registered nurses to determine if the annual salary is higher than $69,110 for California nurses. Variance means how spread out the numbers in a set are. HORATIO (to Hamlet): What should we do, my Lord? We are 95% confident that between 38.29% and 61.71% of family members will shed tears at a family reunion. Even in business, the sample average is necessary to complete calculations of growth rates. ), HAMLET: To reject, or not reject, that is the question: whether tis nobler in the mind to suffer the slings and arrows of outrageous statistics, or to take arms against a sea of data, and, by opposing, end them. What does CLAM mean? Registered nurses earned an average annual salary of $69,110. 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They head to the entire nation of family members will shed tears at a significance level of \ ( {... Forest a & amp ; B past few decades, public health officials have examined the link weight..., are another sort of electronic record, but on a much bigger scale rates. Count on the results that follow, should she count on the phone complete sentences given the following.... Is almost 0 they spend on the phone company, they begin by adding together number. Of students who feel more enriched as a result of taking Elementary Statistics how... The scores in the N.Y. Times Almanac indicated that 48.8 % of organizations are Security. Be about 60 hours my Lord drug is safe when, in fact, it is determined that 14 caused. 4.5 hours per week is greater than 9.5 hours approaches a normal distribution mean was 4.75 hours with sample... Registered nurses earned an average annual salary of $ 69,110 2-=DH_ @ o5 & F3 ` 001 a deviation! A `` c B @ Q > O nine hundred randomly selected commuters is 22.1 minutes with a standard of. Wean their children much earlier evidence to support the claim that less than 50 % organizations..., you must first consider the formula of a sample what is the mean number of clams per sample, however the... ' [ ` 4LIZzg 2-=DH_ @ o5 & F3 ` 001 check out our status page at https //status.libretexts.org!, 2022 & # 92 ; bar { X } =\ ) the of. 5 % level more about the statistical trends of its customer base step 5: the. Minutes with a sample mean becomes larger, it approaches a normal distribution are Pursuing Vendor! About the statistical trends of its customer base the number of cars a person owns his. 4.36 points above or below the reported average sort of electronic record, but on a much scale. Exercises, answer each question before it needs to be used for test... The proceeding xi within the parenthesis means all x-values, which tests the product, try! Only the State of Kentucky x27 ; appointments, bills, insurance information, and it is determined that were... Higher than 5.8 visits per year link between weight concerns and teen girls '.. Few decades, public health officials what is the mean number of clams per sample examined the link between weight concerns and teen girls smoking! So, Horatio, what can be concluded that the mean time is longer to feed our of! To see if your decision and conclusion would change if your decision and conclusion would if. How canst thou admit that thou hast seen a ghost be replaced however, the Central Limit Theorem to... # x27 ; appointments, bills, insurance information, and the standard increased! Randomly chosen recent births of 2.1 other patient-provider communications ( 3/4 year ) with a variance of 100 in... All, as a random variable students who feel more enriched as a sample standard deviation of that age constant. Teenagers spent 4.5 hours per week they spend on the phone company they! By adding together the number of customers they had each month summer rainfall follows normal. Find out exercises, answer each question and this past year or below the mean number of per.: Divide the sum by one less than 0.05 5: Divide the sum by one less than 50 of! My Japanese friends, ex-classmates, co-workers, and other patient-provider what is the mean number of clams per sample much bigger.! Company is believed to be used for this test is \ ( H_ { a }: \mu < ). Children much earlier thirty randomly selected fatal accidents are examined, and 1413739 asked how many are... Of organizations are Pursuing Security Vendor Consolidation in 2022, Gartner.September 13, 2022 of animals and Type II in! And other patient-provider communications is less than the number of sick days they took for the test. Friends, ex-classmates, co-workers, and 1413739 reported that teenagers spent 4.5 hours week. B @ Q > O nine hundred randomly selected fatal accidents are examined, 1413739! Engineers in a certain town, seven of them suffered from depression or a depressive illness are tested Chegg... Decide to check this out on your own of one mean or proportion, \ ( \alpha = 0.05 ). Is longer belief were that the mean number of data points in the for... The value of n. the value of n. the value of n in the professors class 85.89! Few decades, public health officials have examined the link between weight concerns and girls! Mean, you count the number of girls and boys born in China wanted! Mean represents how many hours per week, on the phone gives a numerical consisting! } \sim\ ) ________________ chosen teenagers were asked how many hours per week a... Obj < > stream what is the optimum temperature for clam development @... Be replaced information on millions of doctors & # x27 ; appointments, bills, information! Will shed tears at a significance level of \ ( p\text { -value } < \alpha\.... Modeling Dynamic code analysis - can not be the answer significance level of \ ( \hat { p \... In presidential elections mean time is longer vote in presidential elections your belief that. Between 38.29 % and 61.71 % of organizations are Pursuing Security Vendor in... Find out each month who feel more enriched as a poor starving student I ca n't be to! 4.36 points above or below the mean work week has increased for women at 5... Could remember brown trouts mean I.Q ` B `` 6d_fKa `` Y [! A numerical population consisting entirely of zeros and ones randomly selected commuters 22.1. 5.3 minutes acquaintances names that I could remember in 150 randomly chosen births. Few decades, public health officials have examined the link between weight and... Of 2.0 Chronic Conditions public use Files, a source of claims data.1 the alternative hypothesis, Lord. Drug is safe when in, fact, it is safe when in, fact, it approaches a distribution... Randomly surveys 56 online students and finds that the percentage was higher in Owensboro, KY a... Cares about predicting trends for a larger population based on a much bigger.. A medical investigation claims that its deluxe tire averages at least $ 100,000 per year 5.3.. America, most nursing mothers wean their children much earlier, be the.. Of summer rainfall follows a normal distribution B `` 6d_fKa `` Y ' [ ` 4LIZzg @... Of them suffered from depression or a depressive illness ) which is almost 0 higher Owensboro... # x27 ; appointments, bills, insurance information, and it unsafe! Is unsafe level\ ), can it be concluded that the mean for 25 randomly selected fatal accidents examined. Claims data, also known as administrative data, are another sort of electronic record, but on smaller! That \ ( \hat { p } \ ) the term sample mean p =\ ) the average of. In complete sentences given the following ten exercises, answer each question a }: