Lab10 - STAT 350 Lab #10 For her senior thesis, an...

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STAT 350 – Lab #10 For her senior thesis, an undergraduate in biology wanted to study the effect of crowding (population density) on fecundity (egg production) using Tribolium (flour) beetles. She had 100 jars of flour. She controlled the density (number of beetles per jar) in her experiment and then would measure the number of eggs produced. Dividing the number of eggs by the number of adults would give a measure of the fecundity of the population (she decided it would be impossible to sex all the beetles which is why she is not measuring fecundity as #eggs per female). She used density levels ranging from 100 to 2500 beetles per jar and replicated each density level 4 times. The results of her experiment are given in the accompanying Excel file. All plots and analyses for this lab should be done in SAS. Do not worry about making the plots look "nice". 1. This part you may do in Excel: Get some summary information on the independent ( x ) variable. Find the average density, the variance and standard deviation of the density, and S xx (note – you can get S xx easily from the variance of x ). Average density: d = 1300 Variance of density: s d 2 = 525252.5 Standard deviation of density: s d = 724.7431 S xx (here S dd ): = S dd = ( n -1) s d 2 = 52,000,000 2. One thing that she is interested in is estimating the fecundity when the population density is 1000. Using the 4 observations for fecundity when density was 1000, give a point estimate for the predicted # eggs/female and give a 95% prediction interval ( consider this early review – this has nothing to do with regression ). There were n =4 jars with densities of 1000 beetles. For these 4 jars, the average fecundity was 3.01 with a standard deviation of 1.305322 The point estimate is 3.01 eggs/adult. The resulting prediction interval is then: () 1 3.01 3.182 1.305322 1 4 ±+ (-1.6338, 7.6538) Clearly it is not possible to have negative eggs, so the interval can be adjusted to (0, 7.6538) 1
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3. No transformations. Use density as the independent variable and fecundity as the dependent variable. a. Give the least squares regression equation to predict fecundity from density. f = 9.41530 – 0.00410 d b. Based on this regression analysis, give a point estimate for the predicted # eggs/female and give a 95% prediction interval for the fecundity (# of eggs/adult) when the density is 1000. The predicted fecundity is 9.41530 – 0.00410(1000) = 5.3155 The 95% prediction interval is () 2 1000 1300 1 5.3155 1.96 4.31347 1 100 5200 * 0000 ±+ + (-3.1883, 13.8193) *I used the critical value from the z table because the sample size was quite large. It would also be acceptable (and technically more appropriate) to use a t critical value. With 99 degrees of freedom, the critical t value would be between 1.98 and 2.00. Critical values in that range will also be accepted for this question as well as 4b and 5b.
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This note was uploaded on 03/09/2010 for the course STAT 350 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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Lab10 - STAT 350 Lab #10 For her senior thesis, an...

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