# Sampling Method Assignment

Added on - Nov 2019

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1.Identify the sampling method for each scenario.(a)An orchard farmer subdivides his orchard into 40 parcels of land. He randomly selects 4parcels and inspects every tree on those parcels for the presence of a particular fungus.(b)A librarian inspects every fifth book on a shelf startingwith the second to determine the number of items missing bar codes.(c)A hotel leaves customer satisfaction cards in each guestroom. At the end of the week, the general managerreads all 60 cards that were filled out by guests that week.(d)The College of Engineering randomly selects samples from each of its four branches(mechanical, civil, chemical, electrical) to assess the effectiveness of a new program forstudent advising2.If thecity council were to collect data on householdincomes for its district, one would typically find the distribution to be skewed right.(a)Sketch a histogram that shows a skewed-right distribution.(b)If we are given the values \$43,000 and \$62,000, which is probably the mean and which isthe median? Explain.This is a cluster samplingmethodThis is a systematic samplingmethodThis is censusThis is a stratified samplingmethodSince the distribution isright-skewed \$62,000 isprobably the mean and\$43,000 is probably themedian. In a right-skeweddistribution, the mean isnormally larger than themedian.
3.SAT Math scores tend to follow a bell-shaped distribution with a mean of 515 points and astandard deviation of 114 points.(a)What percent of SAT Math scores is less than 629?(b)What percent of SAT Math scores is between 401and 743?(c)Any student whoseSAT Math score falls in thebottom 2.5% of allscores is immediately disqualifiedfrom considerationfor admission to State U. What isthe cut-off score forthe lowest 2.5% of all scores?We begin by computing thez-scorez=́xμσ=629515114=1P(z<1)=0.8413Thus the percent of SATMath score that is less than629 is 84.13%We begin by computing thez-scorez=́xμσ=743515114=2z=́xμσ=401515114=1P(1<z<2)=0.8185Thus the percent ofSATMath scores is between 401and 743is 81.85%We begin by computing thez-scoreThe z-score equivalent tothe cumulative probability of0.025 (2.5%) is-1.959964Z = --1.959964z=́xμσ=x515114=1.959964x515=1.959964114x=(1.959964114)+515=291.564Thus the cut-offis SAT Mathscores less than292
4.Consider the following data collected from a sample of 12 American black bears:Length (cm)139138139120.5149141141150166151.5129.5150Weight (kg)110609060851009585155140105110(a)Sketch a scatterplot of the data. Treat length as the explanatory variable. Describe theassociation.(b)Construct the equation for the line of best fit. Round your values to 3 decimal places.Length (cm)Weight (kg)xyX2Y21391101529019321121001386082801904436001399012510193218100120.560723014520.253600149851266522201722514110014100198811000014195133951988190251508512750225007225166155257302755624025151.51402121022952.2519600129.510513597.516770.25110251501101650022500121001714.51195173257.5246447.8127625 