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.

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? ABC

Given 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 H0

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: 0.51, 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?