(iii) The sampoo on Alpha and Bravo has the same probability ofworking as with Alpha and Charlie. This probability is 10%.(iv) The sampoo on Bravo and Charlie in 40% of cases works.How likely is it that the shampoo will work on all three mice at thesame time?Hint: use the principle of inclusion-exclusion 4. In an animal experiment, three mice with dandruff in their hair arewashed with hair shampoo. The mice are named Alpha, Bravo andCharlie. From many previous animal experiments, it is known that(i) Alpha, Bravo and Charlie have no dandruff after washing in 30%,45% respectively 65% in most cases they no longer have dandruff.(ii) The shampoo on Alpha, Bravo or Charlie in 95% of the casesworks.

Let us assume the sizes of three sets, |X|,|Y| and |Z|, the size of their intersections areX∩Y,X∩Z…

Answered: 4. In an animal experiment, three mice…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A hospital has studied its patient history and had concluded that 2% of patients that have been admitted have been infected with staff bacteria. Which of the following is true ? -the population proportion p is 0.02 -the population proportion p-hat is 0.02 -the sample proportion p is 0.02 - the sample proportion p-hat is 0.02
In the year 2000, the state of Indiana began a $40-million renovation of its state fairgrounds, which included the building of a miniature golf course and a state- of-the-art livestock building. Now, Indiana officials are interested in learning what sorts of people are visiting the new attractions. In a survey done at this year's state fair, it was found that, among a random sample of 80 couples at the fair with their children, 54 had visited the new miniature golf course, and among an independently chosen, random sample of 65 couples at the fair on a date (without children), 31 had visited the miniature golf course. Based on these samples, can we conclude, at the 0.05 level of significance, that the proportion p, of all couples attending the fair with their children who visited the miniature golf course is different from the proportion p, of all couples attending the fair on a date who visited the miniature golf course? Perform a two-tailed test. Then complete the parts below. Carry…
An antidepressant has historically been known to relieve depression for 80% of patients who use the drug. The drug's formula was changed recently to include a smaller dose of its main, active ingredient. Due to this change, a medical researcher suspects that among all people with depression who use the new version of the drug, the proportion, p, of people who find relief is lower than 80%. A random sample of 245 patients who use the new version is selected by the researcher, and 178 of them find relief from depression. Based on these data, can we support the researcher's claim at the 0.01 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H, :0 H :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO (c)…
Athabasca Fishing Lodge is located on Lake Athabasca in northern Canada. In one of its recent brochures, the lodge advertises that 75% of its guests catch northern pike over 20 pounds. Suppose that last summer 65 out of a random sample of 84 guests did, in fact, catch northern pike weighing over 20 pounds. Does this indicate that the population proportion of guests who catch pike over 20 pounds is different from 75% (either higher or lower)? Use? = 0.05 . Is the sample size large enough to approximate distribution using Normal distribution? WHY?.b. What are the hypotheses?
A postgraduate student studying genetics at Copper belt University was attempting to cross a tiger and a cheetah. He predicted a phenotypic outcome of the traits he was observing to be in the following ratio 4 stripes only: 3 spots only: 9 both stripes and spots. When the cross was performed and he counted the individuals she found 50 with stripes only, 41 with spots only and 85 with both. According to the Chi-square test, did he get the predicted outcome? In your answer include; A possible null hypothesis (H0) that the engineer might have proposed. Clearly show your workings.
An antidepressant has historically been known to relieve depression for 80% of patients who use the drug. The drug's formula was changed recently to include a smaller dose of its main, active ingredient. Due to this change, a medical researcher suspects that among all people with depression who use the new version of the drug, the proportion, p, of people who find relief is lower than 80%. A random sample of 215 patients who use the new version is selected by the researcher, and 159 of them find relief from depression. Based on these data, can we support the researcher's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. H:0 H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value…
According to a study on the effects of smoking by pregnant women on rates of asthma in their children, for expectant mothers who smoke 20 cigarettes per day, 22.2% of their children developed asthma by the age of two in the US. A biology professor at a university would like to test if the percentage is different in another country. She randomly selects 319 women who only deliver one child and smoke 20 cigarettes per day during pregnancy in that country and finds that 82 of the children developed asthma by the age of two. In this hypothesis test, Do the hypothesis test. Use a level of significance of a = 0.05; Use the unrounded values in Excel to find the answers for #3 and #4 1. This is an example of 2. Find the standard error. 3. Find the z value. Question 10 V a hypothesis test.
Many fundraisers ask for donations using email and text messages. A paper describes an experiment to investigate whether the proportion of people who make a donation when asked for a donation by email is different from the proportion of people who make a donation when asked for a donation in a text message. In this experiment, 1.7% of those who received and opened an email request for a donation and 7.8% of those who received a text message asking for a donation actually made a donation. Assume that the people who received these requests were randomly assigned to one of the two groups (email or text message) and suppose that the given percentages are based on sample sizes of 2,000 (the actual sample sizes in the experiment were much larger). (Let p1 be the proportion who make a donation after receiving an email, and p2 be the proportion who make a donation after receiving a text message.) Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to two…
You are interested in testing if there is a difference in weight-loss between 3 popular diet types; low calorie, low fat and low carb. Participants are randomly assigned one of the three groups or a control group. The control group will be told that are participating in a weight-loss study, but will not be following any particular diet. This is to study the placebo effect, weight-loss from just participating in the study. At the start of the study, each participant's weight is recorded in pounds. After 8 weeks they are weighed again, and the weight difference is recorded. A positive value represents a weight loss while a negative value represents a weight gain. Test at 5% significance. Round answers to 3 decimal places. Diet Type Low Calorie Low Calorie Low Calorie Low Calorie Low Calorie Low Fat Low Fat Low Fat Low Fat Low Fat Low Carb Low Carb Low Carb Low Carb Low Carb Control Control Control Control Control Pounds Lost 6.9 4.7 3.5 7.7 5.9 3.8 1.4 3.8 5.2 2 4.9 2.6 2.7 5.6 3.4 1.3…
Mr. Smith continues on his project of gaining insights on the 2020 BIOLOGY class and now that the first test has been written he can get initial findings. Something of interest that he would like to explore is the relationship between marks obtained and the time taken to complete the Test 1. In particular, he wants to answer: what influence does marks obtained have on the amount of time taken to finish the Test 1 . The table below shows a randomly selected sample of results for 12 students: Marks (%) Time (mins) 57 33 67 29 83 26 100 21 23 43 40 43 43 21 47 38 33 44 60 36 57 30 53 40 Use this data to answer the following questions: a. (1) time is the dependent variable or (2) Marks is the dependent variable b. Calculate c. Determine the least squares estimator for i.e, Answer d. (1) Based on the value for , the independent variable does not have an influence on the dependent variable. (2) Based on the value for , an increase of the…
Suppose you were presented with the results of a study comparing two different training methods for basketball athletes. You are told 32 athletes were randomly assigned to the two groups so that 16 were in the group A and 16 were in the group B. At the end of the session, the average scores (wins versus losses) of the two groups/teams were compared and a difference of 10% was observed ( the first team had 10% more wins than the second). The coach observer reports two- sample t-test shows this difference is statistically significant. How would you interpret these findings? What questions or concerns would you have? How might this type of study be improved? Hint: Consider the possibility that the test performed was not the appropriate one.
A random sample of n1 = 157 people ages 16 to 19 were taken from the island of Oahu, Hawaii, and 12 were found to be high school dropouts. Another random sample of n2 = 129 people ages 16 to 19 were taken from Sweetwater County, Wyoming, and 6 were found to be high school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different (either way) from that of Sweetwater County? Use a 1% level of significance. (a) What is the level of significance? What is the value of the sample test statistic? (Test the difference p1 − p2. Do not use rounded values. Round your final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

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