If the pattern of profit and loss does not change in the following months, how many housewives are estimated to prefer each brand at the end of month 2?
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TOPIC: MARKOV CHAINS
A market research firm conducted a household survey regarding preferences for three brands of detergents.
three brands of detergents. The survey was conducted by interviewing the same housewives at the beginning of two consecutive months.
consecutive months. The results of the survey are as follows:
- Beginning of month 1: 200 respondents showed a preference for the "Ace" brand, 120 for the "Bold" brand, and 180 for the "Clean" brand.
for the "Clean" brand.
C) If the pattern of profit and loss does not change in the following months, how many housewives are estimated to prefer each brand at the end of month 2?
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- Ecologists conducted a study to investigate the potential ecological impact of golf courses. Investigators monitored the reproductive success of bluebirds in birdhouses at nine golf courses and ten similar birdhouses at nongolf sites. Data on nests in birdhouses occupied only by bluebirds are shown in the table. If the proportions of nests occupied is the same for golf and nongolf sites, what would be the expected count of birdhouse with 1 nest in nongolf locations? O nests 1 nest Total 2 or 3 nests Golf 30 42 8 80 Nongolf 40 58 22 120 Total 70 100 30 200 50 b 42 60 d. 58 e 40 O O O O OPart A: A researcher wants to determine if there is a relationship between having been to college and preferring cats or dogs. Perform the appropriate test based on the following data: Cats Dogs College 42 52 No College 36 47 (Rows: College. Columns: Cats vs Dogs) Part B: Test the hypothesis that the same proportion of students find the following pet-types to be their favorite. Cats Dogs Rocks Turtles 29 31 26 26A nutrition study investigated knowledge about fruit juices. The study was conducted in a pediatric clinic. Accompanying parents were asked to classify a national brand of “fruit drink”, that contains less than 10% fruit juice, as 100% fruit juice, fruit juice mix, or no fruit juice at all. The investigators asked 150 parents. The table contains the results. Juice Content Gender Female Gender Male Total 100% 15 15 30 1%-99% 55 25 80 0% 30 10 40 100 50 150 The chi‑square statistic for the null hypothesis of independence has: - 6 degrees of freedom. - 3 degrees of freedom. - 2 degrees of freedom. - 4 degrees of freedom.
- A crossover trial is a type of experiment used to compare two drugs. Subjects take one drug for a period of time, then switch to the other. The responses of the subjects are then compared using matched-pair methods. In an experiment to compare two pain relievers, seven subjects took one pain reliever for two weeks, then switched to the other. They rated their pain level from 1 to 10, with larger numbers representing higher levels of pain. The results were: Subject Drug A Drug B 1 6 5 2 3 1 3 4 4 7 6 2 7 4 2 Can you conclude that the mean pain level is less with drug B? Use a=0.05. (1) Critical Value (Round off to 3 decimal places): (2) Test Statistic (Round off to 2 decimal places): (3) Conclusion: (Type 'Reject HO' or 'Fail to Reject HO')Example 1: The owner of a local restaurant chain in town was trying to determine the best location to open her next restaurant and she had narrowed it down to two locations. She wanted to make her decision based on how interested residents in each area were in her restaurant. So she hired an independent company to survey residents from each neighborhood to gauge their interest. In the first neighborhood, 120 residents were surveyed and 84 of them expressed interest in the new restaurant. In the second neighborhood, 200 residents were surveyed and 110 of them expressed interest in the new restaurant. Carry out an appropriate hypothesis test at the a = 0.02 level to determine if there is sufficient evidence to suggest that one neighborhood is more interested in the new restaurant than the other.Dataset: NES. Variables: spend8, nesw.) The NES dataset contains spend8, which records the number of government policy areas where respondents think spending should be increased. Scores range from 0 (the respondent does not want to increase spending on any of the policies) to 8 (the respondent wants to increase spending on all eight policies). The NES, of course, polls a random sample of U.S. adults. In this exercise you will analyze spend8 using the Analyze ▶ Compare Means ▶ One-Sample T Test procedure. You then will draw inferences about the population mean. Make sure you weight observations using the nesw variable so your results are nationally representative. A. The spend8 variable has a sample mean of ______.
- A manufacturing plant makes computer chips 24 hours a day. Employees work one of three, 8 hour shifts during the morning (2am-10am), day (10am-6pm), and night (6pm-2am). Below are data on the number of defective chips on a randomly chosen 24 hour period. Shift Morning Day Night Number of Defective Chips 23 26 47 Total Chips Manufactured 330 330 330 The plant manager thinks there might be more defective computer chips manufactured during the night shift compared to the day shift. Give appropriate statistical evidence to test the managers' claim.At an assembly plant, workers assemble parts for a piece of farm equipment. The supervisor conducted an experiment to compare the effectiveness of three assembly methods, A, B, and C. Eighteen employees were randomly assigned, six employees each, to one of the three methods. After completing their training, each person was asked to assemble five pieces of equipment using his or her training method. The average time to complete the assembly of all five pieces of equipment was recorded. (a) What type of study design is used? O independent groups design O repeated measures design O matched pairs design O randomized block design What are the experimental units in this study? O the 18 employees O the five pieces of equipment to be assembled O the three assembly methods O the average time to assemble five pieces of equipment (b) What are the treatments? O the 18 employees O the five pieces of equipment to be assembled O the three assembly methods the average time to assemble five pieces of…Cable TV choices: A telecommunications company provided its cable TV subscribers with free access to a new sports channel for a period of 1 month. It then chose a sample of 404 television viewers and asked them whether they would be willing to pay an extra $10 per month to continue to access the channel. A total of 35 of the 404 replied that they would be willing to pay. The marketing director of the company claims that the percentage of all of its subscribers who would pay for the channel differs from 6%. Can you conclude that the director's claim is true? Use the a=0.10 level of significance and the P-value method with the table. Part: 0 / 4 Part 1 of 4 (a) State the appropriate null and alternate hypotheses. Ho : H₁ : This hypothesis test is a (Choose one) ▼ test. Part: 1 / 4 Part 2 of 4 P-value= Part: 2 / 4 Part 3 of 4 (b) Compute the P-value. Round the answer to at least four decimal places. (c) Determine whether to reject Ho. (Choose one) Part: 3 / 4 Part 4 of 4 X (d) State a…
- A nutrition study investigated knowledge about fruit juices. The study was conducted in a pediatric clinic. Accompanying parents were asked to classify a national brand of “fruit drink”, that contains less than 10% fruit juice, as 100% fruit juice, fruit juice mix, or no fruit juice at all. The investigators asked 150 parents. The table contains the results. Juice Content Gender Female Gender Male Total 100% 15 15 30 1%-99% 55 25 80 0% 30 10 40 100 50 150 What is the value of the chi‑square statistic for the test of independence for this table? - 7.239 -3.84 -5.156 -1.645Help.A researcher conducted a study to determine whether a new type of phys- ical therapy would help people recovering from knee injuries. The study included 10 patients, and 5 physical therapists. The researcher decided to conduct the experiment using a matched pairs design, as follows: Two patients were (randomly) assigned to each physical therapist. Then, one of the two patients was randomly chosen to receive the new treatment, while the other received the old treatment. After one week, the researcher measured each patient’s improvement in range of motion (ROM), in degrees (◦). (a) Describe the benefit of conducting a matched pairs experiment in this way. (b) The table/image attached to this question shows the data obtained from this experiment: By hand, carry out a t-test to see if the mean difference in ROM improvements between the two treatments (New minus Old) is greater than zero.
