2. A team of wildlife ecologists is interested in the effectiveness of an antifer- tility drug in controlling the growth of pigeon populations. To measure effectiveness, they will estimate the size of the population this year and compare it with the estimated size for a previous year. A large trap is constructed for the experiment. The trap is then baited with a corn feed containing a fixed amount of the drug. An initial sample of t = 120 pi- geons is trapped and allowed to eat the medicated feed. Each bird is then tagged on its leg and released. One week later, they trap a second sample of 50 pigeons. Of these 20 of them have tags. The next day, a third sample of 50 pigeons is trapped. Of these 18 of them have tags. The second sam- ple of 50 pigeons is not released before the trapping of the third sample. Estimate the size of the pigeon population and place a bound on the error of estimation.
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- A purchasing agent obtained 60 watt bulbs from two companies. He has the samples tested in his laboratory for the length of the life with the following results: Length of Life (in hours) 1700 and under 1900 1900 and under 2100 2100 and under 2300 2300 and under 2500 2500 and under 2700 Соmpany A Соmpany B 12 3 14 30 20 17 8 6 2 a. Which Company's bulb do you think are better in terms of average life? b. If price of both types are the same, which company's bulbs would you buy and why? ( Coefficient of variation is Mean /Standard deviation **100)You want to determine the effect of soap on bacterial colonies. In order to make sure that the environmentdoes not affect your experiment, you divide 13 different petri dishes in half - one side is exposed to soap, theother is a control.You measure the number of colonies that grow in each petri dish and come up with the following results:petri dish 1 2 3 4 5 6 7 8 9 10 11 12 13soap 10 5 7 10 19 11 13 17 19 8 11 10 16control 20 17 11 17 26 18 21 25 24 17 17 17 21Perform a complete hypothesis test to see if there is a difference in bacterial colonies between the soapand control dishes.Again - notice that you are given no advice. You need to figure this out on your own, althoughthis one should be a bit easier than (4). Feel free to use R to solve this problem, just make sureyou don't just hand in a printout.A randc v ection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms, 15 of them were given multivitamin tablets daily which contain 3 grams of vitamin C and various other vitamins and minerals. The remaining 15 volunteers were given placebo tablets. For each individual, the length of time taken to recover from cold is recorded. At the end of the experiment following data are obtained: Days to recover from cold Treated with multivitamin 3.0, 3.2, 6.3, 3.8, 5.8, 7.3, 5.3, 5.7, 7.9, 5.7, 6.2, 4.3, 3.8, 6.1, 4.6 Treated with placebo 7.1, 5.9, 5.5, 5.2, 2.4, 3.7, 4.9, 3.5, 4.3, 6.6, 4.5, 3.2, 3.4, 4.1, 2.9 Send data to calculator v It is known that the population standard deviation of recovery time from cold is 1.8 days when treated with multivitamin, and the population standard deviation of recovery time from cold is 1.5 days when treated with placebo tablets. It is also known that both populations are approximately…
- A psychologist would like to examine the effects of sugar consumption on the activity level of preschool children. Three samples of children are selected with n = 5 in each sample. One group gets no sugar, one group gets a small dose, and the third group gets a large dose. The psychologist records the activity level for each child. The data from this experiment are presented below. No sugar Small dose Large dose 3 6. 3 3 8 1 7 G = 60 1 4 2 EX? = 298 3 4 T = 15 T = 20 T = 25 SS = 16 SS = 12 SS = 20 A) Solve for, Critical F: = B) Do these data indicate any significant differences among the three groups? Test with a = .05. C) Do you reject or fail to reject Ho and why? ABCGiven a random sample of size n from a uniform population with a = 0, find an estimator for ß by the method of moments.Prices of diamonds are very sensitive to their weight (measured in carat). For example, the price of a 1 carat diamond tends to be much higher than the price of a 0.99 carats diamond. To study this phenomenon in more detail, we consider two random samples of diamonds, 0.99 carats and 1 carat, each sample of size 23. The average price of 0.99 carats diamonds in the sample is $4451, while the average price of 1 carat diamonds in the sample is $5681. From long-term studies, we know that both the prices of 0.99 carats diamonds and the prices of 1 carat diamonds are normally distributed with standard deviations oj = $1332 (0.99 carats) and o2 = $1613 (1 carat), respectively. (a) Carry out a hypothesis test at significance level 0.01 to evaluate whether the true average price µi of 0.99 carats diamonds is lower than the true average price µ2 of 1 carat diamonds. Specify Ho and Ha, the test statistic, and calculate the p-value or use p-value considerations to conclude. (b) Compute the type II…
- A student decides to spin a dime and determine the proportion of times it lands on heads. The student spins the dime 25 times and records that it lands on heads 17 times. Let p = the true proportion of times the dime would land on heads when spun. Under the assumption that the true proportion is 0.5, 100 simulated proportions for samples of size 25 are shown in the dotplot. Using the dotplot, what do the two dots above 0.70 represent? There is a 2 in 100 chance that the true proportion of heads is 0.7. In two simulated samples of 25 spins, the proportion of heads is 0.7. There is a 2 in 100 chance that the sample proportion of heads is 0.7. In two simulated samples of 25 spins, the true proportion of heads is 0.7.A farmer has decided to use a new additive to grow his crops. He divided his farm into 10 plots and kept records of the corn yield (in bushels) before and after using the additive. The results are shown below. Plot 1 2 3 4 5 6 7 8 9 10 Before 9 9 8 7 6 8 5 9 10 11 After 10 9 9 8 7 10 6 10 10 12 You wish to test the following hypothesis at the 5 percent level of significance. H0:Population mean d=0 against h1:population mean d <0 What is your decision about H0Have you ever been frustrated because you could not get a container of some sort to release the last bit of its contents? An article reported on an investigation of this issue for various consumer products. Suppose five 6.0 oz tubes of toothpaste of a particular brand are randomly selected and squeezed until no more toothpaste will come out. Then each tube is cut open and the amount remaining is weighed, resulting in the following data: 0.51, 0.63, 0.42, 0.5, 0.35. Does it appear that the true average amount left is less than 10% of the advertised net contents? USE SALT (a) Check the validity of any assumptions necessary for testing the appropriate hypotheses. O The sample was randomly selected and the normal probability plot is not acceptably nonlinear. The sample was selected to represent a range of results and the normal probability plot is not acceptably nonlinear. The sample was selected to represent a range of results and the normal probability plot is not acceptably linear. O…
- Have you ever been frustrated because you could not get a container of some sort to release the last bit of its contents? An article reported on an investigation of this issue for various consumer products. Suppose five 6.0 oz tubes of toothpaste of a particular brand are randomly selected and squeezed until no more toothpaste will come out. Then each tube is cut open and the amount remaining is weighed, resulting in the following data: 0.52, 0.63, 0.43, 0.5, 0.35. Does it appear that the true average amount left is less than 10% of the advertised net contents? USE SALT (a) Check the validity of any assumptions necessary for testing the appropriate hypotheses. O The sample was selected to represent a range of results and the normal probability plot is not acceptably nonlinear. O The sample was selected to represent a range of results and the normal probability plot is not acceptably linear. The sample was randomly selected and the normal probability plot is acceptably linear. O The…Phosphorous is a chemical that is found in many household cleaning products. Unfortunately, phosphorous also finds its way into surface water, where it can harm fish, plants, and other wildlife. Two methods of phosphorous reduction are being studied. At a random sample of 7 locations, both methods were used and the total phosphorous reduction (mg/L) was recorded. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. Things that are labelled i underneath a b c, etc are all part of that part.Hotel prices worldwide are projected to increase by 3% next year (Lodging Magazine website, June 15, 2016), but is there a difference between Europe and the U.S.? Suppose we have projected changes in hotel costs for 47 randomly selected major European cities and 53 randomly selected major U.S. cities. These data are provided in the DATAfile IntHotels. Use α= .01 What is the p-value?.What is your conclusion?