|An experiment was conducted to study the life (in hours) of two different brands of batteries in three different brands of batteries in three different devices (radio, camera, and portable DVD player). A completely randomized two-factor experiment was conducted and the following data resulted. Device Brand of Battery Radio Camera DVD Player 8.6 7.9 5.4 8.2 8.4 5.7 Everbluey 8.3 8.3 5.6 8.4 8.1 5.3 9.4 8.5 5.8 8.8 8.9 5.9 Muracell 8.7 9 5.7 9.2 8.4 5.8 Analyze the data and draw conclusions. Use alpha = 0.05 Which brand of battery would you recommend using? 00| 00| 00
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- What is meant by the sample space of an experiment?What is an experiment?An experiment was conducted to study the life (in hours) of two different brands of batteries in threedifferent devices (radio, camera, and portable DVD player). A completely randomized two-factorexperiment was conducted, and the following data resulted.Brand Deviceof Battery Radio Camera DVD PlayerA 8.6 7.9 5.48.2 8.4 5.7B 9.4 8.5 5.88.8 8.9 5.9(a) Analyze the data and draw conclusions, using α = 0.05. (b) Investigate model adequacy by plotting the residuals. (c) Which brand of batteries would you recommend?
- A study published in 2007 by Christopher Johnson, professor of music education and music therapy at the University of Kansas, revealed that students in elementary schools who took private music lessons scored around 20 percent higher in math scores on standardized tests, compared to students who did not take private music lessons. Is this a randomized experiment or an observational study? a) Randomized experiment, since researchers gave students standardized tests. b) Observational study, since whether the student took private music lessons was not randomly assigned. c) Observational study, since math scores were not randomly assigned. d) Observational study, since this was not a random sample.In randomized, double-blind clinical trials of a new vaccine, children were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the second dose, 116 of 651 subjects in the experimental group (group 1) experienced fever as a side effect. After the second dose, 73 of 532 of the subjects in the control group (group 2) experienced fever as a side effect. Does the evidence suggest that a higher proportion of subjects in group 1 experienced fever as a side effect than subjects in group 2 at the α=0.10 level of significance? #1 Find the test statistic for this hypothesis test.In randomized, double-blind clinical trials of a new vaccine, rats were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the second dose, 111 of 670 subjects in the experimental group (group 1) experienced drowsiness as a side effect. After the second dose, 68 of 551 of the subjects in the control group (group 2) experienced drowsiness as a side effect. Does the evidence suggest that a higher proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the α=0.05 level of significance? a. Find the test statistic for this hypothesis test. Round to two decimal places as needed.
- Patients immobilized for a substantial amount of time can develop deep vein thrombosis (DVT), a blood clot in a leg or pelvis vein. DVT can have serious adverse health effects and can be difficult to diagnose. On its website, drug manufacturer Pfizer reports the outcome of a study looking at the effectiveness of the drug Fragmin (dalteparin) in preventing DVT in immobilized patients. Of the 1518 randomly chosen immobilized patients given Fragmin, 42 experienced a complication from DVT. Of the 1473 randomly chosen immobilized patients given a placebo, 73 experienced a complication from DVT. Compute the proportion (risk) of patients experiencing DVT complications for immobilized patients treated with Fragmin. (Enter the proportion with 4 decimal places. DO NOT enter the percent.)In a study of the effectiveness of a new device that supports a weak or damaged heart, 150 people who consented to treatment were assigned at random to either a standard treatment consisting of drugs or the experimental treatment that consisted of drugs and surgery to install the new device. After two years, 60% of the 67 patients who received the device had improved and 40% of the patients who received the standard treatment had improved. Does this data provide convincing evidence that the proportion of patients who recieved the experimental treatment who improved is higher than for the patients who received the standard treatment? Test the relevant hypotheses using a significance level of 0.05. (Use pexperimental − pstandard ).A) State the null and alternative hypotheses. H0: pe − ps = 0, HA: pe − ps ≠ 0 H0: pe − ps = 0, HA: pe − ps < 0 H0: pe − ps = 0, HA: pe − ps > 0 B) Find the test statistic.z = C) What is the p-value?P-Value = D) State your conclusion in terms of…A consumer preference study involving three different bottle designs (A, B, and C) for the jumbo size of a new liquid laundry detergent was carried out using a randomized block experimental design, with supermarkets as blocks. Specifically, four supermarkets were supplied with all three bottle designs, which were priced the same. The following table gives the number of bottles of each design sold in a 24-hour period at each supermarket. If we use these data, SST, SSB, and SSE can be calculated to be 586.1667, 421.6667, and 1.8333, respectively. Results of a Bottle Design Experiment Supermarket, j Bottle Design, i 1 2 3 4 A 16 14 1 6 B 33 30 19 23 C 23 21 8 12 (a&b) Test the null hypothesis H0 that no differences exist between the effects of the bottle designs and supermarkets on mean daily sales. Set α = .05. Can we conclude that the different bottle designs have different effects on mean sales? (Round F to 2 decimal places and SS, MS to 3 decimal places.…
- In 2010, a medical research group reported the results of an experiment to evaluate the effectiveness of acupuncture to treat a chronic intestinal condition. A group of volunteers with the chronic intestinal condition agreed to participate in the experiment and be randomly assigned to either a true acupuncture treatment or a placebo treatment. The placebo treatment mimicked the application of acupuncture, but no needle penetrated the skin. Random assignment resulted in 78 subjects receiving acupuncture and 75 subjects receiving the placebo treatment. After receiving 6 treatments over the course of 3 weeks, patients were asked to report whether they had experienced a reduction in the chronic intestinal condition. The table summarizes the data from the study, with expected cell counts in parentheses. Yes No Total Acupuncture 41 (37.2) 37 (40.8) 78 Placebo treatment 32 (35.8) 43 (39.2) 75 Total 73 80 153 Which of the following is true about the chi-square test for…Late Night Eating It is well-known that lack of sleep impairs concentration and alertness, and this might be due partly to late night food consumption. A study74 took 44 people aged 21 to 50 and gave them unlimited access to food and drink during the day, but allowed them only 4 hours of sleep per night for three consecutive nights. On the fourth night, all participants again had to stay up until 4 am, but this time participants were randomized into two groups; one group was only given access to water from 10 pm until their bedtime at 4 am while the other group still had unlimited access to food and drink for all hours. The group forced to fast from 10 pm on performed significantly better on tests of reaction time and had fewer attention lapses than the group with access to late night food. What are the explanatory and response variables? Is this an observational study or a randomized experiment? Can we conclude that eating late at night worsens some of the typical effects of sleep…Bicycle frames can be made from carbon, steel, or othermaterials. Carbon frames are much more expensive thansteel, but they are also much lighter. Could this lighter frame have a significant impact on speed? In 2010 a doc-tor in England, who commutes daily to work 27 miles roundtrip on a bicycle, ran his own randomized experi-ment to investigate. Each day for several months Dr. Groves flipped a coin todetermine whether he would ride his steel frame bicycle orhis carbon frame bicycle to work and back. He rode a totalof 30 journeys on the steel frame bike and 26 journeys onhis carbon frame bicycle, recording his total commutingtime for each day. The summary statistics are shown below:a) Why would you prefer to see the actual data beforeproceeding with inference?b) Construct and interpret a 95% confidence interval forthe difference in average commuting times.c) Explain in this context what “95% confidence”means.d) Based on your confidence interval, do the doctor’sdata provide evidence…