Probabilities question:-
Social interaction of mental patients. The Community Mental Health Joumal (Aug. 2000) presented the results of a survey of over 8,000 clients of the Department of Mental Health and Addiction Services (DMHAS) in Connecticut. One of the many variables measured for each mental health patient was frequency of social interaction (on a 5-point scale, where 1 = very infrequently, 3 = occasionally, and 5 = very frequently). The 8.681 clients who were evaluated had a mean social interaction score of 2 95 with a standard deviation of 1.10. a. Conduct a hypothesis test (at a = .01 ) to determine whether the true mean social interaction score of all Connecticut mental health patients differs from 3. b. Examine the results of the study from a practical view, and then discuss why "statistical significance" does not always imply "practical significance." c. Because the variable of interest is measured on a 5-point scale, it is unlikely that the population of ratings will be normally distributed. Consequently, some analysts may perceive the test from part a to be invalid and search for alternative methods of analysis. Defend or refute this position.For each of the following rejection regions, sketch the sampling distribution of f and indicate the ocation of the rejection region on your sketch: 3. f> 1.440. where of = 6 b. * 2.060, where of = 25Increasing hardness of polyester composites. Polyester resins reinforced with fiberglass are used to fabricate wall panels of restaurants. It is theorized that adding cement kiln dust (CKD) to the polyester composite will increase wall panel hardness. In a study published in Advances in Applied Physics (Vol. 2. 2014). hardness (joules per squared centimeters) was determined for three polyester composite mixtures that used a 40% CKD weight ratio. The hardness values were reported as 83. 84, and 79 jom Research has shown that the mean hardness value of polyester composite mixtures that use a 20% CKD weight ratio is p - 76j/em In your opinion. does using a 40% CKD weight ratio increase the mean hardness value of polyester composite mixtures? Support your answer statistically.Minimizing tractor skidding distance. Refer to the Journal of Forest Engineering (July 1999) study of minimizing tractor skidding distances along a new road in a European forest. The skidding distances (in meters) were measured at 20 randomly selected road sites. The data (saved in the SKIDDING file) are repeated in the accompanying table. Recall that a logger working on the road claims that the mean skidding distance is at least 425 meters. Is there sufficient evidence to refute this claim? Use a = .10. 488 350 | 457 109 285 409 435 574 439 546 385 205 184 261 273 400 311 |312 141 |425 Based on Tujek, J. and Pacola, E. "Algorithms for skidding distance modeling on a raster Digital Terrain Model." Joumal of Forest Engineering . Vol 10, No. 1. July 1999. Conclusions and Consequences for a Test of Hypothesis True State of Nature Conclusion HO True Ha True Correct decision Accept HO (Assume HO True) Reject HO Type II error (probability 5) (Assume Ha True) Type I error Correct decision (probability a)Dissolved organic compound in lakes. The level of dissolved oxygen in the surface water of a lake is vital to maintaining the lake's ecosystem. Environmentalists from the University of Wisconsin monitored the dissolved oxygen levels over time for a sample of 25 lakes in the state (Aquatic Biology, May 2010). To ensure a representative sample, the environmentalists focused on several lake characteristics, including dissolved organic compound (DOC). The DOC data (measured in grams per cubic meters) for the 25 lakes are listed in the table on p. 400. The population of Wisconsin lakes has a mean DOC value of 15 grams/m . Use a hypothesis test (at " = .10) to make an inference about whether the sample is representative of all Wisconsin lakes for the characteristic dissolved organic compound Data for Exercise 8.70 Lake DOC Allequash 9.6 Hip Muskellunge 4.5 Hrown 13.2 Crampton 4.1 Cranberry Bog 22.6 Crystal 2.7 FasiLong 14.7 Helmet 3.5 Hiawatha 13.6 Hummingbird 19.8 Kickapoo 14.3 Little Arbor Vitae 56.9 Mary 25.1 Muskellunge Northgate Bog 2.7 Paul 4.2 Peter 30.2 Plum 10.3 Reddington Bog 17.6 Sparkling 24 Tenderfoot 17.3 Trout Bog 38.8 Trout Lake 3.0 Ward 5.8 West Long 7.6 Hasad on Langman, Q C, cial "Control of dissolved anygen in northern temperate lakes over wakes ranging from minutes In days" Aquatic Biology, Vol 9, May 2010 (Table 1).Walking straight into circles. When people get lost in unfamiliar terrain, do they really walk in circles, as is commonly believed? To answer this question, researchers conducted a field experiment and reported the results in Current Biology (Sept. 20, 2000). Fifteen volunteers were blindfolded and asked to walk as straight as possible in a certain direction in a large field. Walking trajectories were monitored every second for 50 minutes using GPS and the average directional bias (degrees per second) recorded for each walker. The data, saved in the CIRCLES file, are shown in the table (next column). A strong tendency to veer consistently in the same direction will cause walking in circles. A mean directional bias of 0 indicates that walking One-Sample T. BIAS trajectories were Variable Mean SoDev SE Mean 954 CI I F BIAS 0.085 1.603 0. 414 1-0.902, 0.972) 0.21 0.410 random. Consequently, the researchers tested whether the true mean bias differed significantly from 0. A MINITAB printout of the analysis is shown below. a. Interpret the results of the hypothesis test for the researchers. Use o = .10 b. Although most volunteers showed little overall bias, the researchers produced maps of the walking paths showing that each occasionally made several small circles during the walk. Ultimately, the researchers supported the "walking into circles" theory. Explain why the data in the table is insufficient for testing whether an individual walks into circles -4.50 -1.00 -0.50 -0.15 0.00 0.01 0.02 0.05 0.15 0.20 0.50 0.50 1.00 2.00 3.00 Based on Souman, J. L., Frissen, I., Sreenivasa, M. N., and Ernst, M. O. "Walking straight into circles." Current Biology , Vol. 19, No. 18. Sept. 29, 2009 (Figure 2).Lengths of great white sharks. One of the most fearedpredators in the ocean is the great white shark. It is knownthat the white shark grows to a mean length of 21 feet;however, one marine biologist believes that great whitesharks off the Bermuda coast grow much longer owing tounusual feeding habits. To test this claim, some full-growngreat white sharks were captured off the Bermuda coast, measured, and then set free. However, because the captureof sharks is difficult, costly, and very dangerous, only threespecimens were sampled. Their lengths were 24. 20, and 22feet. Do these data support the marine biologist's claim ato = .10?For the binomial sample sizes and null-hypothesized values of p in each part, determine whether the sample size is large enough to use the normal approximation methodology presented in this section to conduct a test of the null hypothesis HD: p = p0. a. n = 500, p0 =.05 b. n = 100, p0 =.99 c. n = 50, p0 =.2 d. n = 20, p0 =.2 e. n = 10, p0 =.4Suppose a random sample of 100 observations from a binomial population gives a value of p =.60 and you wish to test the null hypothesis that the population parameter p is equal to.75 against the alternative hypothesis that p is less than.75. a. Noting that p =.80, what does your intuition tell you? Does the value of p appear to contradict the null hypothesis? b. Use the large-sample z-test to test HO: p =.75 against the alternative hypothesis Ha: p<.75. use d=".05." how do the test results compare with your intuitive decision from part a c. find and interpret observed significance level of you conducted in b.packaging children health food. junk foods potato chips are typically packaged to appeal children. can similar packaging healthy food product influence desire consume this was question interest an article published journal consumer behaviour fictitious brand product-sliced apples smiling cartoon apple on front package researchers showed sample schoolchildren asked each whether he or she willing eat product. willingness measured scale at all willing. data summarized as follows: t="3.69," x="2.44," suppose know that mean actual sliced is not for a. conduct determine true exceeds make conclusion. b. values normally distributed. does affect validity conclusion explain.dating disclosure. refer adolescence study adolescents disclosure their dating romantic relationships. recall high school students recruited participate study. one variables adolescent mother where tell always sampled had score standard deviation hypothesize will exceed believe formal hypothesis using o=".01" did voluntarily disclose information about relationships parents research some many student were age gender experience dates extent which his parent being issue late daters stayed out responses last variable categorized tell. identify type variable. unclear exactly selected stating only government classes primarily european american middle-class district. based what potential caveats inferences order iq. international team economists investigated possible link between birth cesifo economic studies source medical registry norway. it known iq stanines norway residents points. who later families points sufficient evidence conclude lower than country w="01" measure reliability inference.bone fossil humerus bones same species animal tend have approximately lengthto-width ratios. when fossils discovered archeologists often by examining length-to-width ratios bones. exhibits ratio unearthed archeological site east africa believed lived. unknown species. length-towidth listed following table saved file. population particular differs practical implications method gas turbines. during periods demand electricity-especially hot summer months-the power output turbine engine drop dramatically. way counter cooling inlet air turbine. increasingly popular uses high-pressure fogging. performance turbines augmented fogging joumal engineering heat rate per kilowatt hour rates gasturbine file next table. has average kj high- pressure i error ii error.>
