what is the mean number of clams per sample

Based on the data shown, what can be concluded about the comparative health of Forest A & B? C. carnivo # of developing calms B. Math Statistics A city claims that the mean number of public transportation users per day is at least 4,800. The phone company records the following values for each of the six months: Add values together. He paces the large room. Subtract the sample mean from each value. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Type II error: We conclude that the mean starting salary is at least $100,000 when, in fact, it is less than $100,000. at least 20%, when in fact, it is less than 20%. Type II error: We conclude that the duration of paid vacations each year for Europeans is six weeks when, in fact, it is not. Type II error: We conclude that the proportion of high school seniors who get drunk each month is 29% when, in fact, it is not 29%. The class took a random sample of 30 freshman students and found a mean study time of 137 minutes with a standard deviation of 45 minutes. Login . $2.02 !!! Between January and February, the provider saw a drastic drop of 2,000 customers in only one month, which was followed by more substantial spikes. In complete sentences, also give three reasons why the two polls might give different results. the tree's development. Suppose the null hypothesis is the drug is unsafe. What is the Type II Error? Your statistics instructor claims that 60 percent of the students who take her Elementary Statistics class go through life feeling more enriched. An instructor thinks the mean age for online students is older than 26.6. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is less than four years old. Suppose you believe that the mean time is longer. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. 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. Dalmatians that fetched the most shekels. HAMLET: That you must teach me. Conduct a hypothesis test to determine if the percent at her school is less than 40%. The women get tired from all of the chats. Finally, the equation asks you to divide by n, which stands for the total number of values that you are comparing. The size of the answer describes how large the variance is in the set. Conclusion: At the 5% significance level, there is insufficient evidence to conclude that the mean number of sick days is not ten. The sample mean of the phone companys customer base over six months is 20,792. Determine the value of n. The value of n in the equation for sample mean represents how many items are being compared. (Polonius turns to Hamlet.) The teenagers would look, stare, and compare. As a poor starving student I don't have much money to spend for even the bare necessities. The solution sheet is found in [link]. Let $P =$ the proportion of friends that has a pierced ear. Claims databases collect information on millions of doctors' appointments, bills, insurance information, and other patient-provider communications. Conduct a hypothesis test to determine if 68% represents California. Do not reject $H_{0}$: There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin. The following questions were written by past students. Sixty-three said they smoked to stay thin. Thus the Central Limit Theorem applies to $\hat{p}$. Conduct a hypothesis test to determine if the rate is still 14% or if it has decreased. The good thing about claims data is that, like other medical records, they come . The sample mean was 18.1 with a sample standard deviation of 1.3. Filter by: Select category from list. I usually use the test program X, which tests the product, to try to create a specific problem. A particular line of business has three types of claims. Conclusion: There is sufficient evidence to support the claim that less than 50% of his friends have pierced ears. The STANDS4 Network . [Z( %H49WA3P%h@ } Use $p=0.90$, corresponding to the assumption that the retailers claim is valid. You decide to check this out on your own. Ninety-five high school and college students I did ask. When clamped, a number will either keep its own value if living in the range imposed by the two other values, take the lower value if initially lower than it, or the higher one if initially higher than it. IMPAQ International LLC, November 2011. http://www.impaqint.com/sites/default/files/research-briefs/Chronic_Conditions_PUF_Brief_Final.pdf, National Library of Medicine Confirm that the sample is large enough to assume that the sample proportion is normally distributed. The first step of finding a sample mean asks us to add all the values in the sample together. Thirty randomly selected fatal accidents are examined, and it is determined that 14 were caused by driver error. A group of researchers think this is not accurate and want to show that the number of public transportation users is less than 4,800 Identify the null hypothesis, Ho, and the alternative hypothesis, Ha , in terms of the parameter . To understand the meaning of the formulas for the mean and standard deviation of the sample proportion. (After all, as a poor starving student I can't be expected to feed our class of animals! . Suppose a study was done to determine if the mean work week has increased. Find the probability that the mean time spent studying per week is greater than 9.5 hours. For large samples, the sample proportion is approximately normally distributed, with mean $_{\hat{P}}=p$ and standard deviation $\sigma _{\hat{P}}=\sqrt{\frac{pq}{n}}$. The sample mean is also useful for calculating sample variance, standard deviation, and standard error. . Theplus-4s confidence interval (see chapter 8) is $(0.3861, 0.6139)$. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. The mean $_{\hat{P}}$ and standard deviation $_{\hat{P}}$ of the sample proportion $\hat{P}$ satisfy. The mean number of cars a person owns in her lifetime is not more than ten. There is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is less than 20%. 72 What is the mean number of clams per sample? Assume the amount of summer rainfall follows a normal distribution. A survey in the N.Y. Times Almanac finds the mean commute time (one way) is 25.4 minutes for the 15 largest US cities. 1. The clearest advantage of calculating the sample mean is that it can provide information thats accurately applicable to a larger population. A sample is large if the interval $\left [ p-3\sigma _{\hat{p}},\, p+3\sigma _{\hat{p}} \right ]$ lies wholly within the interval $[0,1]$. Use the information from the data table below to create a proper scientific graph and to answer the corresponding questions. You dont have to be a statistician to benefit from the use of sample means. >> Whenever a $p\text{-value}$ based on a normal approximation is close to the level of significance, the exact $p\text{-value}$ based on binomial probabilities should be calculated whenever possible. 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. Information and translations of CLAM in the most comprehensive dictionary definitions resource on the web. To see how, imagine that every element of the population that has the characteristic of interest is labeled with a $1$, and that every element that does not is labeled with a $0$. %%EOF No votes so far! 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. What does CLAMS mean as an abbreviation? State the null and alternative hypotheses. He continues by solving for the variance among the test grades. Here are formulas for their values. The cost of a daily newspaper varies from city to city. {qibXMdT -LL42UR&g++Ki5V,lp. How To Calculate Cost of Goods Sold (With Examples), How To Calculate Margin Of Error (With Examples), Shareholder Equity: Definition And Examples, What Is Annual Percentage Rate (APR)? At a 1% level of significance, an appropriate conclusion is: Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. Step 5: Divide the sum by one less than the number of data points in the sample. All Computing (1) Governmental (1) Management (1) Products (1) Art (1) Educational (1) Religion (1) Software (2) Law & Legal (1) Military (1 . It conducts its own survey. By . stream A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening midnight showing of the latest Harry Potter movie. The number of sick days they took for the past year are as follows: 12; 4; 15; 3; 11; 8; 6; 8. What Is Gender Bias In A Job Description? A report by the Gallup Poll found that a woman visits her doctor, on average, at most 5.8 times each year. His tutor, Polonius, is reprimanding Hamlet regarding the latters recent experience. Let $\bar{X}$ the average I.Q. Population mean. So why cant man catch brown trout? Suppose you believe that the brown trouts mean I.Q. What does CLAM mean? In most distributions, all the values will be within two standard deviations of the mean unless it is an outlier. << /Type /Page /Parent 3 0 R /Resources 6 0 R /Contents 4 0 R /MediaBox [0 0 841.8898 595.2756] So could you please try this problem to see if you object? 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. One minute they're happy, another they'll pout. Let $P =$ the proportion of family members who shed tears at a reunion. (With Examples). << /Length 5 0 R /Filter /FlateDecode >> Bethesda, MD 20894, Web Policies The sample mean is represented mathematically as x. Its considered a jumping-off point for initiating further analysis. When youre only looking at a sample group, however, you use the term sample mean. State a consequence of committing a Type I error. Test to see if the proportion has dropped for this generation. Why? x+TT(TH-JN-()MQ( The action you just performed triggered the security solution. The sample standard deviation is 1.8. So my favorite and main staple food is macaroni and cheese. A study was done to test the claim that the mean cost of a daily newspaper is $1.00. She randomly surveys 361 schoolmates and finds that 135 report they fear public speaking. 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. The sample mean is the same as the mean of the population distribution, however, the variance is much greater in the smaller sample size and small for large sample sizes. Polonius enters and places some books upon the table just a moment before Horatio enters.). 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. 20,000+18,000+20,400+21,050+23,000+22,300 = 124,750. The student academic groups claim appears to be correct. The sample mean was 83; the sample standard deviation was ten. An Introduction to Statistics class in Davies County, KY conducted a hypothesis test at the local high school (a medium sizedapproximately 1,200 studentssmall city demographic) to determine if the local high schools percentage was lower. Private universities mean tuition cost is more than $20,000 per year. A student believes that less than 40% of students at her school fear public speaking. Theplus-4s confidence interval is (0.0022, 0.0978). Of the 150 students surveyed, 82 have smoked. Step 6: Take the square root of the variance to get the standard deviation. (In general, you must first prove that assumption, however.). At a significance level of $a = 0.05$, what is the correct conclusion? Reason for decision: The $p\text{-value}$ is greater than 0.05. As a result of the contingents survey, would you agree with the Newsweek poll? 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. Types of Graphs - Meet Mrs. Weber! GARTNER is a registered trademark and service mark of Gartner, Inc., and/or its affiliates in the U.S. and internationally and is used . You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. To recognize that the sample proportion $\hat{p}$ is a random variable. le) Approximately how many clams would be developing in 10 degree Celsius water? The US Department of Energy reported that 51.7% of homes were heated by natural gas. In China, the birth ratio is 100: 114 (46.7% girls). The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at least 11.52 inches. 51.91.103.92 Type I error: We conclude that the mean number of cars a person owns in his or her lifetime is more than 10, when in reality it is not more than 10. Ai, Akemi, Akiko, Ayumi, Chiaki, Chie, Eiko, Eri, Eriko, Fumiko, Harumi, Hitomi, Hiroko, Hiroko, Hidemi, Hisako, Hinako, Izumi, Izumi, Junko, Junko, Kana, Kanako, Kanayo, Kayo, Kayoko, Kazumi, Keiko, Keiko, Kei, Kumi, Kumiko, Kyoko, Kyoko, Madoka, Maho, Mai, Maiko, Maki, Miki, Miki, Mikiko, Mina, Minako, Miyako, Momoko, Nana, Naoko, Naoko, Naoko, Noriko, Rieko, Rika, Rika, Rumiko, Rei, Reiko, Reiko, Sachiko, Sachiko, Sachiyo, Saki, Sayaka, Sayoko, Sayuri, Seiko, Shiho, Shizuka, Sumiko, Takako, Takako, Tomoe, Tomoe, Tomoko, Touko, Yasuko, Yasuko, Yasuyo, Yoko, Yoko, Yoko, Yoshiko, Yoshiko, Yoshiko, Yuka, Yuki, Yuki, Yukiko, Yuko, Yuko. Let $P =$ the proportion of students who feel more enriched as a result of taking Elementary Statistics. Conduct a hypothesis test of your belief. What is the possible proportion of patrons that do borrow books from the Owensboro Library? (Hamlet resignedly attends to his task.). 5 0 obj The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. Conduct a hypothesis test. The organization thinks that, currently, the mean is higher. new individuals are formed by a combination of two ____ cells. The Type I error is to conclude that the percent of EVC students who attended is ________. is 4. An online retailer claims that $90\%$ of all orders are shipped within $12$ hours of being received. 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. less than 20%, when in fact, it is less than 20%. Most common CLAMS abbreviation full forms updated in October 2022. $H_{0}: \mu \geq 11.52$ $H_{a}: \mu < 11.52$. She received her BA in psychology from Hunter College. An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. The final step to figuring out a sample mean is to input the values youve determined into the original equation and divide to solve. Follow the steps below to determine the variance of a sample set. You conduct a study. NDE: Non-Dual Eligible; DE: Dual-Eligible; CC: Chronic Condition, 1Erdem, Erkan. 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. 1. Out of 76 Americans surveyed, only two had seen or sensed the presence of an angel. Round to two decimal places as needed.) $H_{0}: \mu \geq 150$ $H_{0}: \mu < 150$. 4980 0 obj <>stream I went to 53 of the closest grocery stores and surveyed the prices of macaroni and cheese. Type II error: We conclude that the mean is 34 years, when in fact it really is not 34 years. 10Hs Biology_End-of-Term Assessment_Revision Sheet 23- Clams were placed into various temperatures of water. Canned clams. The average number of bubbles would be at least 22. Hypothesis testing: For the following ten exercises, answer each question. Why? ), "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. CHAT. Conduct a hypothesis test. The sample mean is 4 4 4 4 pencils. The result is called the variance. The plus-4s confidence interval is $(0.411, 0.648)$. Answer any other questions asked in the problem. 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. According to the N.Y. Times Almanac the mean family size in the U.S. is 3.18. Before my God, I might not this believe, without the sensible and true avouch of mine own eyes. Nine out of 70 randomly chosen N.Y. City residents reply that they smoke. ___________________________________________________, 2. For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. The Austin, TX chamber of commerce feels that Austins commute time is less and wants to publicize this fact. It has a mean $_{\hat{P}}$ and a standard deviation $_{\hat{P}}$. Using the value of $\hat{P}$ from part (a) and the computation in part (b). A random sample of 10 weeks had a mean number of 17.7 infections. The proceeding xi within the parenthesis means all x-values, which would be the values for each piece of data youre investigating. Type II error: We conclude that the proportion of women who develop breast cancer is at least 11%, when in fact it is less than 11%. Additionally, the sample mean is used in a variety of different industries. She surveys 84 of her students and finds that 11 attended the midnight showing. (However, they are very close.). \[\hat{p} =\frac{x}{n}=\frac{102}{121}=0.84\nonumber\], \[\sigma _{\hat{P}}=\sqrt{\frac{(0.90)(0.10)}{121}}=0.0\overline{27}\nonumber\], \[\left [ p-3\sigma _{\hat{P}},\, p+3\sigma _{\hat{P}} \right ]=[0.90-0.08,0.90+0.08]=[0.82,0.98]\nonumber\]. if in a sample of $200$ people entering the store, $78$ make a purchase, \[\hat{p}=\dfrac{78}{200}=0.39. This means checking that the interval, \[\left [ \hat{p}-3\sqrt{\frac{\hat{p}(1-\hat{p})}{n}},\, \hat{p}+3\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \right ]\]. The number 124,750 represents the total number of customers that the phone provider had over the six-month sample size. Am I right? One hundred fifty students were chosen at random and surveyed. endobj Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. Does the Almanac result remain valid? 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. Population mean is unknown. At the 5% level of significance, there is enough evidence to conclude that 48.8% of families own stocks. The sample mean is defined as the average of a given sample set. What is the optimum temperature for clam development? "The Problem with Angels," by Cyndy Dowling. What is the mean number of clams per sample? The test scores were for the class were: (82, 88, 83, 89, 91, 79, 85, 93, 83). Not to conclude the drug is safe when, in fact, it is safe. After four years the girls were surveyed again. This gives a numerical population consisting entirely of zeros and ones. Reason for decision: $p\text{-value} < \alpha$. While the sample mean will give information about the average of a sample and variance measures the difference between each value in the sample, the standard error is slightly different. The sample proportion is the number $x$ of orders that are shipped within $12$ hours divided by the number $n$ of orders in the sample: Since $p=0.90$, $q=1-p=0.10$, and $n=121$. Ironically, I work for a company that sells products with known problems. Assuming the retailers claim is true, find the probability that a sample of size $121$ would produce a sample proportion so low as was observed in this sample. 4 0 obj 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? The sample average was $71,121 with a sample standard deviation of $7,489. Based on the answer to part (c), draw a conclusion about the retailers claim. In words, define the random variable for this test. At $\alpha = 0.05$ level, is the class mean family size greater than the national average? To begin this process, they must determine the sample mean. Population mean \textbf{a. Note that here the large-sample $1 - \text{PropZTest}$ provides the approximate $p\text{-value}$ of 0.0438. She randomly surveys 56 online students and finds that the sample mean is 29.4 with a standard deviation of 2.1. The best estimate of the population mean is sample mean X \bar{X} X which is 20 . What is it called when you make predictions about data not yet recorded? Here are the data I wrote in my notebook: I could see that the cost varied but I had to sit down to figure out whether or not I was right. Sixty-eight percent of online courses taught at community colleges nationwide were taught by full-time faculty. This is also known as the distribution rate. The student academic group on a college campus claims that freshman students study at least 2.5 hours per day, on average. The mean number of years Americans work before retiring is 34. This page titled 6.3: The Sample Proportion is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. HORATIO (to Hamlet): What should we do, my Lord? Primary 2 0 obj Do not reject $H_{0}$: There is not sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin. Before attempting to solve for your organizations sample mean, you must first consider the formula. (Some are repeats.) She surveys 84 of her students and finds that 11 of them attended the midnight showing. Unfortunately, most of the problems are difficult to create, which makes them difficult to fix. Using $\alpha = 0.05$, is the AAA proportion accurate? To better understand the process of finding a sample mean, consider the steps in terms of the following example. of a set of brown trout. A battery manufacturer claims that the lifetime of a certain battery has a . \[\begin{align*} P(0.33<\hat{P}<0.43) &= P\left ( \frac{0.33-\mu _{\hat{P}}}{\sigma _{\hat{P}}}
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