1. (a) A cert ain company sends 40% of its overnight mail parcels via express mail service b1. Of these parcels, 4% arrive late (after the guar nteed delivery time). If a record of m over night mailing is rm do mly selected from the compmy's file, what is the probability th at the par cel went via E and was late? Su ppose th at 50% of the overnight parcels are sent via express mail service E2 (b) and the rem aining 10% are sent via E3. Of those sent via E2, only 3% arrive lat e, whereas 6% of the parcels handled by Ea arrive late. Wh at is the probability that a randomly select ed parcel a rived late?
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A: given P(E1)=0.4 P(L/E1)=0.04
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- A company selling home furnaces claims that installingtheir new high efficiency furnace will “cut your heating bill in half.” A consumer agency collects data for a ran-dom sample of homes and plots this year’s heating costs with the new furnaces against previous costs with the oldfurnaces. Which are the most appropriate hypotheses totest the company’s claim?A) H0: b = 0, HA: b ≠ 0B) H0: b = 0, HA: b 7 0C) H0: b = 0, HA: b 6 0D) H0: b = 0, HA: b 6 0.5E) H0: b = 0.5, HA: b ≠ 0.5If a study determines the difference in average salary for subpopulations of people with blue eyes and people with brown eyes is NOT significant, then the populations of blue-eyed people and brown-eyed people are ________ different salaries. a) unlikely to have b) very unlikely to have c) guaranteed to have d) guaranteed to not haveSO what would be the L, Lq, and Wq of this problem? Assuming we are trying to develop and sovle a waiting line system that can accomodate this increased leel of passenger traffic.
- 3. Each of a group of 20 intermediate tennis players is given two rackets, one having nylon strings and the other synthetic gut strings. After several weeks of playing with the two rackets, each player will be asked to state a preference for one of the two types of strings. Let p denote the proportion of all such players who would prefer gut to nylon, and let X be the number of players in the sample who prefer gut. Because gut strings are more expensive, consider the null hypothesis that at most 50% of all such players prefer gut. We simplify this to H0: p = .5, planning to reject H0 only if sample evidence strongly favors gut strings. (a) Is a significance level of exactly .05 achievable? If not, what is the largest α smaller than .05 that is achievable? (b) If 60% of all enthusiasts prefer gut, calculate the probability of a type II error using the significance level from part (a). Repeat if 80% of all enthusiasts prefer gut. (c) If 13 out of the 20 players prefer gut, should H0 be…A graduate student realized that the depression study above in Question 4 should have had a placebo condition in which a third group was given a pill just as the people in the Drug condition were, but where the pill was not Drug D (e.g., a sugar pill). So she designed a new experiment with three conditions -- Drug, No Drug, and Placebo. To perform the experiment, the graduate student randomly assigned 18 people into the three groups so that each group has 6 people. After one month of treatment, all 18 people were asked to rate on a scale from 1 to 7 how depressed they felt, where 1 = not depressed at all and 7 = very depressed. The following are the data: Drug No Drug Placebo 2 4 5 3 5 5 4 5 6 4 4 5 2 6 4 3 6 5 nD = 6 nND = 6 nplacebo = 6 MD = 3 MND = 5 Mplacebo = 5 Using an α-level of .05, perform an…From historical data at a local restaurant indicate that 60% of customers order coffee, 15% order soft drinks, and the remaining order water. The owner of the restaurant is planning on opening a new restaurant for the purpose of stocking enough of various drinks, wants to know if the proportions are the same for his new restaurant as they were for his original restaurant. In a sample of 1000 customers at the new restaurant, 550 ordered coffee, 190 order soft drinks, and the remaining simply wanted water. At the 5% level of significance, does it appear the proportions have changed?
- In a clinical study, a random sample of 540 participants agree to have their blood drawn, which is to be examined for the presence of antibodies against a certain contagious disease. It is found in 22% of the blood samples, which experimenters hope to extrapolate to the general population. From this random sample, 10 participants' blood samples are selected at random. If X is the number of samples out of the 10 who have these antibodies, what can we say about X? A. The sample size is not large enough for us to approximate X using a normal distribution B.The expected value of X is 22 C. X can be approximated using a normal distribution in lieu of a binomial distribution D. X has a sampling distribution that is normalA disgruntled employee of a prominent delivery company in Baltimore County is accused of adding water into the fuel tanks of a large fleet of delivery vehicles. The manager asked the guard who observed the act to walk the parking lot with him to identify a sample of vehicles closer to the guards' booth. Upon returning to his office, the manager figured that since all the vehicles were of the same color, same engine size, and were on an inventory purchased and delivered just about the same year when all the previously existing vehicles were sold away, the decision to include the entire fleet for testing prior to filing the police report. The vehicles inventory could be described as . . .In a Japanese study, “researchers looked at 35 peoplewith lower back pain who were enrolled in an aquatic exercise program, which included swimming and walk-ing in a pool. Almost all of the patients showed improve-ments after six months, but the researchers found that those who participated at least twice weekly showedmore significant improvement that those who wentonly once per week.”Which of the following statements is true?a) This experiment proves that swimming causes areduction in lower back pain.b) This study is a poorly designed experiment sincethere is no control group and no randomization.c) Conclusions based on this observational study aresuspect since participation in the aquatic programmay be confounded with other lifestyle behaviors thatmay cause the improvement in lower back health.d) Conclusions based on this observational study aresuspect since a sample size of 35 is too small.e) This study is not an observational study since theaquatic program is a treatment.
- 4.(a) The manufacturer of a certain voltmeter claims that 95% or more of its readings are within0.1% of the true value. In a sample of 500 readings, 470 were within 0.1% of the truevalue. Is there enough evidence to reject the claim?(b) A manufacturer of computer workstations is testing a new automated assembly process.The current process has a defect rate of 5%. In a sample of 400 worksations assembled bythe new process, 15 had defects. Can it be concluded that new process has a lower defectrate?Q15) A cookie jar containts 15 chocolate chip and 5 oatmeal cookies. If 3 cookies are randomly selected, what is the probablity at least one is an oatmeal cookie? (Find TWO METHODS to calculate this problem, and show the work)