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Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card | 8th Edition | ISBN: 9781464158933 | Authors: David S. Moore, George P. McCabe, Bruce A. Craig ISBN: 9781464158933 206

Solution for problem 2.60 Chapter 2

Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card | 8th Edition

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Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card | 8th Edition | ISBN: 9781464158933 | Authors: David S. Moore, George P. McCabe, Bruce A. Craig

Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card | 8th Edition

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Problem 2.60

Whats wrong? Each of the following statements contains a blunder. Explain in each case what is wrong. (a) There is a high correlation between the age of American workers and their occupation. (b) We found a high correlation (r 1.19) between students ratings of faculty teaching and ratings made by other faculty members. (c) The correlation between the gender of a group of students and the color of their cell phone was r 0.23.

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Preferred Mineral Orientation *How does preferred mineral orientation develop *Pressure solution­occurs in wet rocks at low T. *Minerals dissolve at compressed faces *Minerals grow where compression is less *Grains become shorter, parallel to compression. *Plastic deformation occurs at higher T. *Existing grains flatten by deforming internally *Shear Rotation and Flattening *Shear flattens grains in a manner similar to compression *Shear rotates grains into alignment Kinds of Metamorphic Foliation *Slaty Cleavage *Low Grade: alignment of clay minerals *Schistosity: *Medium­high grade: alignment of large micas *Compositional bonding(Gneissic bonding) *High grade: light bands of felsic minerals and dark bands of mafic minerals Intensity of Metamorphism *Rock type related to intensity Slate low grade Phyllite Schist Gneiss High grade Transition from shale to slate *Both rocks are extremely fine grained *Metamorphism and deformation cause clay minerals to recrystallize to micas and reorient into a strongly planar fabric, giving the product a near perfect ‘slaty cleavage.’ Transition from Shale to Phyllite *Micas continue to recrystallize and grow larger (yet not visible to the naked eye) *The texture of the rock becomes less perfectly planar. Phyllites in hand sample appear wavy and shiny Transition from Phyllite to Schist *Recrystallization reactions make micas, quartz and feldspar large enough to see in hand sample. *The rock is still strongly foliated (from the dominance by micas) and commonly has porphyroblasts of minerals like garnet and Al­Silicates. Transition from Schist to Gneiss *At higher P and T, micas begin to break down, forming minerals like garnet, feldspar and Al­ Silicates. *These reactions coupled with the mechanical difference between micas and quartz + feldspar produce the banded appearance of gneiss *Gneiss and schists both have visible grains, but schists are dominated by micas and gneiss has characteristic banding Formation of Foliation *Foliation more pronounced, crystals larger when metamorphism is more intense *Clays  Micas  Feldspar Migmatite *Many gneiss are called migmatites­ mixed rocks that combine metamorphic and igneous (melted) components. (very high grade metamorphism mainly sedimentary protoliths) *The facing stone on funnel, cooper and hart hall are made of migmatite Sedimentary Protoliths Protolith Metamorphic equivalent Conglomerate (or breccia) Metaconglomerate Sandstone (all types) Quartzite Shale Slate…phyllite…schist…gneiss Grade: Low…medium…high Limestone Marble Sandstone v. Quartzite *Grains in clastic sedimentary rocks are cemented together and the cement is ordinarily somewhat weak *When these rocks are metamorphosed, the first things to go is the cement *Grains are literally ‘fused’ together, make a densely interlocking frame work of grains Limestone v Marble *Why are most limestones dull and often dark in color whereas most marbles are bright white *And where do those streaks in some types of marble come from *The dark color of limestones comes partly from incorporated clastic material (clays) and organic matter. *The metamorphic process boils out the volatile organics making a lighter color rock, and when clays recrystallize during deformation, the new minerals formed take on folded, contorted and streaked patterns Progressive Metamorphism *Note that basically the same textural changes occur if the protolith is a clay­rich sediment or a fine­grained igneous rock. The specifics for the igneous protoliths, however, are different… Green Stones *At low grades, glass and many igneous minerals in extrusive (volcanic) rocks commonly recrystallize to form fine grained green micas and amphiboles *Greenstones are green because the original igneous minerals have recrystallized forming green metamorphic minerals Amphibolite *Greenstones taken to higher metamorphic grades are course grained rocks called amphibolite. *These can be massive, garnet­bearing rocks, as seen at Gore Mountain in the Adirondacks or… ordinary looking gneisses. *Unlike gneisses with sedimentary protoliths, amphibolites are made up mainly of amphibole (not mica) Metamorphic Grade *Prograde­ metamorphism via increasing T and P *Common in rocks that are buried in organic belts *Progressive changes *Recrystallization results in new mineral assemblages *Mineral changes release water *Retrograde­Metamophism via decreasing T and P *Common in rocks that are brought from depth by erosion or exhumation *Requires addition of H2O by hydrothermal fluids *Without added water, retrograde reactions cannot occur *Many metamorphic rocks preserve prograde conditions Metamorphic Facies *Mineral assemblages from a specific protolith at specific P and T conditions *Create rocks that are predictably similar *Named for a dominant mineral Index Minerals *Index Minerals indicate a specific P and T range *Useful for identifying P and T history *Index mineral maps *Define metamorphic zones *Boundaries are isograde Metamorphic Environments *Metamorphism occurs in different settings *Different settings yield to different effects via *Variation in the geothermal gradient *Changing gradients of different stresses *Variability in the nature of hydrothermal fluids *These characteristics are governed by plate tectonics *Types (and Settings) of metamorphism *Thermal: heating by plutonic intrusion *Burial: Increases in P and T by deep burial in a basin *Dynamic: Shearing in a fault zone *Regional: P and T alteration due to orogenesis *Hydrothermal: Alteration by hot water leaching *Subduction: High P, low T altercation *Shock: Extreme high P attending a bolide impact Thermal (Contact) Metamorphism *Due to heat from magma invading host rock *Creates zoned bonds or alteration in host rock *Called a contact or metamorphic aureole *The aureole surrounds the plutonic intrusion *Zoned from high (near pluton) to low grade (far from pluton) *Grades of alteration form aureoles around the pluton *Bands range from highly altered to increased heating *The width of each aureole zone is due to: *The size of the plutonic intrusion *The degree of metasomatism *The dominant rock is hornfels Burial Metamorphism *As sediments are buried in a sedimentary basin *P increases because of the weight of the overburden *T increases because of the geothermal gradient *Requires burial below diagenetic effects *This is ~8­15km depending on the geothermal gradient Dynamic Metamorphism *Breakage of rock by shearing at a fault zone *Fault location determines type of alteration Shallow crust­upper 10­15km *Rocks behave in a brittle fashion *Mineral grains crush forming fault breccia Deeper crust­Below 10­15km *Rocks are ductile *Minerals smear like taffy to form mylonite Regional Metamorphism *Tectonic collisions deform huge “mobile belts” *Directed compression thickens mountains *Rocks caught up in a mountain building are *Heated via the geothermal gradient and plutonic intrusions *Squeezed and heated by deep burial *Smashed and smeared by differential stresses *Regional metamorphism creates foliated rocks *This type of metamorphism is, by far, the most important in terms of the amount of rock altered *Collisional belts are often: *Thousands of km long *Hundreds of km wide Hydrothermal Metamorphism *Alteration by hot, chemically aggressive water *A dominant process near mid­ocean ridge magma *Cold ocean water seeps into fractured crust *Heated by magma, this water then reacts with mafic rock *The hot water rises and is ejected via black smokers Subduction Metamorphism *Subduction creates the unique blue schist facies *Trenches and accretionary prisms have: *A low geothermal gradient (low T, high P) *These conditions favor glaucophane, a blue amphibole mineral Shock Metamorphism *Rarely, Earth is struck by a comet or asteroid *Impacts generate a compressional wave *Extremely high pressure *Heat that vaporizes or melts larger masses of rock *These conditions generate high pressure minerals Exhumation *How do metamorphic rocks return to the surface *Exhumation is due to uplift, collapse and erosion Finding Metamorphics *Large regions of ancient high­grade rocks­ called shields­ are exposed in continental interiors *Shields are eroded remnants of organic belts *Shield rocks form the basement under sedimentary cover Geological Structures *Wherever you see sedimentary rocks that aren’t lying horizontally these rocks have been DEFORMED in some large­scale process *It’s important to try to imagine the scale of the entire structure to which a single area or outcrop belongs Deformation *As a result of plate tectonics, the crust is constantly under stress *Rocks respond to stress by deforming *Deformation may be brittle, in which rocks will tend to break, or ductile in which rocks will tend to flow or bend ­Temperature ­Pressure ­Deformation Rate ­Composition *Displacement: change in location *Rotation: Change in Orientation *Distortion: Change in Shape Types of Stress *There are three principle types of stress 1) Compressive 2) Tensional 3) Shear **Pressure isn’t the same as stress Traces of Stress in Rocks *By measuring objects of known undeformed dimensions, we can estimate the nature and magnitude of deformation. Brittle Deformation *Brittle deformation breaks rocks *When rock breaks and no movement takes place then it is a fracture *When rock on the sides of the fracture move then it is a fault Describing Orientation of Geologic Features with Strike and Dip **A planar structures orientation can be specified by strike and dip STRIKE: Angle between an imaginary horizontal line on the structure and the direction of true north. DIP: Angle of the structures slope Fault Orientation *We classify faults based on direction of movement of individual blocks, with reference the Earth’s surface (horizontal) *On a dipping fault, the blocks are classified as the *Hanging­wall block (above the fault) AND *Footwall block (Below the fault) *Standing in a tunnel excavated along the fault *Your head, is near the hanging­wall block *you are standing on the footwall block Fault Classification *Fault geometry varies­vertical, horizontal, dipping *The relative motion of the offset block varies *Dip slip: blocks move parallel to dip of the fault *Strike­slip: blocks move parallel to fault plane strike *Oblique slip: components of both dip slip and strike slip Dip­Slip Faults *Sliding is parallel to the dip of the fault *Blocks move up or down the slope of the fault *The two kinds of dip­slip fault depend on relative motion *Reverse fault: the hanging wall moves up the fault slope ­Thrust fault (a special type of reverse fault) *Normal fault: the hanging wall moves down the fault slope Normal Faults *The hanging wall moves down relative to the footwall Reverse and Thrust Faults *The hanging wall moves up relative to the footwall *Reverse faults: Fault is steeper than 35 degrees *Thrust faults: fault deep is less than 35 degrees *Accommodate crustal shortening (compression) Thrust Faults *Place older rocks on top of younger rocks *Common at the leading edge of orgenic deformation *Can transport thrust sheets hundreds of kilometers *Act to shorten and thicken mountain belts Strike­Slip Faults *Fault motion is parallel to the strike of the fault *Usually vertical, no hanging wall­footwall blocks *Classified by the relative sense of motion *Right lateral: opposite blocks move to observer’s right *Left lateral: opposite blocks move to observers left *Large strike­slip faults may slice the entire crust Faults *Faults may offset large blocks of Earth *The amount of offset is a measure called displacement *The San Andres displacement of hundreds of Km Fault Recognition *Continuous features are displaced across a fault *Faults may juxtapose different kinds of rock *Friction may bend rocks near the fault into drag folds *Brittle faulting results in shattered and crushed rock *Fault breccia consists of rock fragments along a fault *Fault gouge is made of polarized, powdered rock *Scarps are visible when faults intersect the surface *Fault zones with breccia and gouge preferentially erode *Ductile faults create plastically deformed rocks *Rocks don’t break, instead they are intensely sheared *Rocks from ductile shear zones are called mylonites *Mylonites typify detachment faults in collisional orogens Fault Systems *Faults commonly occur in groups called fault systems *Due to regional stresses that create many similar faults *May diverge from a common horizontal detachment fault

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Chapter 2, Problem 2.60 is Solved
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Textbook: Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card
Edition: 8
Author: David S. Moore, George P. McCabe, Bruce A. Craig
ISBN: 9781464158933

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