Torsion during hip external rotation and extension may explain why acetabular labral tears occur in professional athletes. The article “Hip Rotational Velocities During the Full Golf Swing” (J. of Sports Science and Med., 2009: 296–299) reported on an investigation in which lead hip internal peak rotational velocity (x) and trailing hip peak external rotational velocity (y) were determined for a sample of 15 golfers. Data provided by the article’s authors was used to calculate the following summary quantities:
Separate normal probability plots showed very substantial linear patterns.
- a. Calculate a point estimate for the population
correlation coefficient . - b. Carry out a test at significance level .01 to decide whether there is a linear relationship between the two velocities in the sampled population.
- c. Would the conclusion of (b) have changed if you had tested appropriate hypotheses to decide whether there is a positive linear association in the population? What if a significance level of .05 rather than .01 had been used?
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Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
- The spike stature of the plants grown from the seeds of the porcine separates (Dactylis glomerata L) collected from the University campus and İbradı Eynif pasture are given below. In this plant, compare whether there is a difference between regions in terms of spike height. Virgo Height (cm) Data obtained from plants collected from university campus 5 6 8 7 8 6 5 5 4 6 6 Data obtained from plants collected from Eynif pasture 12 9 11 9 9 11 9 10 11 10 Note: Your results interpretation according to two different possibilities (Do it separately, assuming that it is 0.07 and 0.04).arrow_forwardONLY THE LAST ONE Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.5 6.8 6.5 7.0 6.3 7.9 9.0 8.4 8.7 7.8 9.7 7.4 7.7 9.7 8.2 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.5 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.3 7.8 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.9 Prior to obtaining data, denote the beam strengths by X1, . . . , Xm and the cylinder strengths by Y1, . . . , Yn. Suppose that the Xi's constitute a random sample from a distribution with mean μ1 and standard deviation σ1 and that the Yi's form a random sample (independent of the Xi's) from another distribution with mean μ2 and standard deviation σ2. (a) Use rules of expected value to show that X − Y is an unbiased estimator of μ1 − μ2. E(X − Y) = E(X) − E(Y) = μ1 − μ2 E(X − Y) = E(X) − E(Y) 2 = μ1 − μ2 E(X − Y) = nm E(X) − E(Y) = μ1 − μ2 E(X −…arrow_forwardFind kurtosis by using ungroup data given in the picture using quartile deviation, make sure to arrange data before solving question.arrow_forward
- The authors of the paper "Dynamics of Canopy Structure and Light Interception in Pinus elliottii, North Florida" (Ecological Monographs (1991):33-51) planned an experiment to determine the effect of fertilizer on a measure of leaf area. A number of plots were available for the study, and half were selected at random to be fertilized. In order to assure that the plots to receive the fertilizer and the control plots were similar, prior to beginning the experiment tree density (the number of trees per hectare) was recorded for six plots to be fertilized and six control plots, resulting in the given data. Do the plots differ in tree number? Do you have any concerns about their experimental design? Fertilizer plots 1320 1216 1312 1280 1216 1312 control plots 1104 1072 1088 1150 1272 1280arrow_forwardLow-Birth-Weight Hospital Stays. Data on low-birthweight babies were collected over a 2-year period by 14 participating centers of the National Institute of Child Health and Human Development Neonatal Research Network. Results were reported by J. Lemons et al. in the on-line paper “Very Low Birth Weight Outcomes of the National Institute of ChildHealth and Human Development Neonatal Research Network” (Pediatrics, Vol. 107, No. 1, p. e1). For the 1084 surviving babies whose birth weights were 751– 1000 grams, the average length of stay in the hospital was 86 days, although one center had an average of 66 days and another had an average of 108 days. a. Can the mean lengths of stay be considered population means? Explain your answer.b. Assuming that the population standard deviation is 12 days, determine the z-score for a baby’s length of stay of 86 days at the center where the mean was 66 days.c. Assuming that the population standard deviation is 12 days, determine the z-score for a…arrow_forwardIn which situation cointegration test can be performed? Write down its null Also, refer the given table and interpret the results?arrow_forward
- The propagation of fatigue cracks in various aircraft partshas been the subject of extensive study in recent years.The accompanying data consists of propagation lives(flight hours/104) to reach a given crack size in fastenerholes intended for use in military aircraft (“StatisticalCrack Propagation in Fastener Holes Under SpectrumLoading,” J. Aircraft, 1983: 1028–1032):.736 .863 .865 .913 .915 .937 .983 1.0071.011 1.064 1.109 1.132 1.140 1.153 1.253 1.394a. Compute and compare the values of the sample meanand median.b. By how much could the largest sample observationbe decreased without affecting the value of themedian?arrow_forwardFind kurtosis using quartile deviation.arrow_forwardData from the Motor Vehicle Department indicate that 80% of all licensed drivers are older than age 25. In a sample of n=50 people who recently received speeding tickets, 33 were older than 25 years and the other 17 were age 25 or younger. Is the age distribution for this sample significantly different from the distribution for the population of licensed drivers? Use alpha=0.5. A. what is the proposed analysis and why you chose this? B. Test assumptions and make a decision with evidence? C. Inferential statics and P values? D. Final decision and Conclusion?arrow_forward
- Determine the kurtosis if the data given is a sample.arrow_forwardAssume that last year in a particular state with 700000 children there were 1552 children out of 31500 in a random sample who were diagnosed with Autism Spectrum Disorder. Nationally, 1 out of 88 children are diagnosed with ASD. Is there sufficient data to show that the incident rate of ASD is higher in that state than nationally? Test at the 7% level.P: PARAMETER What is the correct parameter symbol for this problem? What is the wording of the parameter in the context of this problem? H: HYPOTHESES Fill in the correct null and alternative hypotheses: The value of p on this one is a fraction....leave it exact. H0:H0: HA:HA: A: ASSUMPTIONS Since information was collected from each object, what conditions do we need to check? Check all that apply. n(1−pˆ)≥10n(1-p̂)≥10 σσ is unknown. N≥20nN≥20n np≥10np≥10 σσ is known. n(1−p)≥10n(1-p)≥10 n≥30n≥30 or normal population.…arrow_forwardGiven the data in the following table for wave-solderingnonconformities, determine if there are any differencesbetween the two processes. Based on variousa levels, would you recommend a change to the proposedprocess?arrow_forward
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