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- 1. A phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phylum. A simple random sample of 50 alga is obtained and each alga is categorized as either being a cyanobacterium or not. The researcher found that 40 alga were, in fact, cyanobacteria. (enter your answer in 3 decimal places) (a) What is the sample proportion of the algae that were cyanobacteria? (b) What is the standard deviation of the sample proportion of the algae that were cyanobacteria?(c) What is the 95% marginal error of the proportion of the algae that were cyanobacteria?(d) What is 95% CI? , wattsSuppose you rolled a fair six-sided die a few times and recorded the results. (You would have a collection of numbers 1-6.) Now, suppose you wanted to average these numbers. What value would you expect? If the die was rolled 6 times and the results were: 1, 4, 2, 2, 3, 2, then the average of this sample of rolls would be 2.333. This experiment could be peformed again: 6, 5, 2, 1, 1, 4. Now, the average of this sample is 3.167. Obviously, these small samples have a lot of variation in them; however, is there a way to calculate the expected average? If we were to construct a very large sample, rolling this die 1 million times, what would the expected value (mean) be? Luckily, the rules of probability allows us to do this calculation without actually having to roll the die 1 million times! Below, you will find a probability table where all of the possible outcomes from the die are listed. The first column contains the possible outcomes on the die, the second column contains the…A bag contains three different balls, one red (r), one blue(b), one white(w). TWO balls are drawn from the bag without replacement one after the other (at random without looking) and the colors recorded. This means once the first color is drawn, the first ball is kept out of the bag and only 2 colors remain when the second ball is drawn. List the sample space. [Use lower case letters for the colors, preserve the given order, commas separating pairs, no spaces.]
- An advertising agency wants to know whether the no of column inches of classified ad carried by 2 competing newspapers is equal. The no of column inches appearing in both newspapers, respectively, on 20 randomly selected days follows: 663 & 725, 713 & 806, 626 & 620, 682 & 626, 639 & 595, 651 & 614, 769 & 744, 701 & 719, 723 & 680, 670 & 639, 665 & 602, 639 & 657, 694 & 624, 614 & 614, 651 & 583, 632 & 682, 739 & 657, 657 & 639 & 775 & 745. Use signed-rank test at 0.01 level of sig to test to test whether or not newspaper 1 & 2 carry equal amount of classified ad. What is the z value and decision?4. A newspaper story claims that more houses are purchased by singles now than singles 5 years ago. To test this claim, two studies were conducted on the buying habits of singles over the past 5 years. In the first study, 200 house purchases in the current year were randomly selected and 80 of those were made by singles. In the second study, again 200 house purchases were randomly selected from 5 years ago and 57 of those were made by single people. Test the newspaper's claim using a 0.05 level of significance. Is there sufficient evidence to support the newspaper's claim? Let singles now be Population 1 and let singles 5 years ago be Population 2. Step 1. State the null and alternative hypotheses for the test. Fill in the blank below. A) Step 2. Compute the value of the test statistic. Round your answer to two decimal places. Step 3. Draw a conclusion and interpret the decision. A) We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level…Suppose that a simple random sample of n = 2 numbers will be selected from the list of values 10, 12, 14, 16, 18. (a) There are ten possible equally likely samples of n 2 numbers that could be selected (10 and 12, 10 and 14, etc.). Calculate the sample mean for each sample. = Sample 10, 12 Sample 12, 16 I 10, 14 12, 18 10, 16 14, 16 10, 18 12, 14 14, 18 16, 18 (b) Summarize the results of part (a) into a table showing the sampling distribution of possible sample means. To do this, list each possible value for the sample mean along with the probability the value would occur. (Enter your answers from smallest to largest value for the sample mean.) Probability
- The assets (in billions of dollars) of the four wealthiest people in a particular country are 46, 33, 21, 12. Assume that samples of size n = 2 are randomly selected with replacement from this population of four values. a. After identifying the 16 different possible samples and finding the mean of each sample, construct a table representing the sampling distributi- of the sample mean. In the table, values of the sample mean that are the same have been combined. Probability Probability x 46 39.5 33.5 33 29 (Type integers or fractions.) CITR X 27 22.5 21 16.5 12A population consists of a batch of 24,683 aspirin tablets, and it includes 1,050 that are defective because they do not meet specifications. A random sample of n = 200 of the tablets is obtained and tested, with the result that 15 of them are defective. a. What is the population proportion, p, of defective aspirin tablets? b. What is the sample proportion, p, of defective tablets? c. How can the discrepancy between the population proportion and the sample proportion be explained? a. The population proportion of defective aspirin tablets is p = (Round to three decimal places as needed.) b. The sample proportion of defective aspirin tablets is p= (Round to three decimal places as needed.) c. Choose the correct answer below. C O A. There will always be a discrepancy between the population proportion and the sample proportion when the sample size is small. O B. Random samples collected with sound sampling methods vary, and the sample proportions differ from the population proportion…1. A lawn mower company will produce 1,500 lawn mowers by 2020. In an effort to determine how much maintenance free consumers will take when they already buy lawn mowers, the company decided to conduct a study over the past 1 year of these mowers. . First, a random sample was taken by contacting 200 grass mowers. The company owner provides an 800 number and is asked to contact the company when the first repair is needed for the lawn mower. Owners who no longer use lawn mowers to cut their grass are either disqualified or not sampled. After 1 year, it turned out that 187 owners had reported for the first repair. However, the other 50 disqualified themselves. The average number per year until the first improvement was 5.3 times for samples deemed feasible. It is believed that the standard deviation is 1.28 per year. If the company wants to advertise the lawnmower and with a confidence level of 95%, what is the estimated annual mean value of repair-free lawn mower for this lawn mower?…
- The geographical distribution of the hometown of 80 students of PUP is given as: 50 from Luzon, 10 from Visayas, and 20 from Mindanao. (1) How many ways can three students be selected at random such that NO student comes from Luzon and Mindanao.(2) How many ways can three students be selected at random such that all of them come from any of the three places.1. Suppose there are nine sections of Intro Stats with 25 students each. You ‘randomly’ choose two studentsfrom each section to use as asample. Which of the following results best describes this type of sample?A. a random, stratified sampleB. a simple random sampleC. a random, clustered sampleD. a non-random, systematic sampleE. a random, convenient sample 2. Suppose there are nine sections of Intro Stats with 25 students each. You place all 225 student’s namesin a hat and ‘randomly’ draw 30 student names to use as asample. Which of the following results bestdescribes this type of sample?A. a random, stratified sampleB. a simple random sampleC. a random, clustered sampleD. a non-random, systematic sampleE. a random, convenient sample 3. Assume the heights of students at College are normally distributed with a mean of 64.0 inchesand a standard deviation of 1.2 inches. Which of the following values best approximates the probabilityof randomly selecting aCollege student tallerthan 62.2…3)For equal varainces cases, if N1 is sample size of sample 1 and N2 is sample size of smaple 2, then total DF is equal to?" N1+N2-2 N1+N2-1 N1-N2 N1+N2
