Blog

A random sample of n = 200 observations is selected from a binomial population.  The sample estimate of the proportion of successes is 0.13.  Using a significance level of α = 0.10, we want to test: Ho:  p = 0.10 Ha:  p > 0.10 Assuming that we can use large-sample procedures, calculate the value of the test statistic needed to test these hypotheses.

A plant breeder develops a new wheat variety she hopes will yield more in the plains than the three most popular varieties under dry-land farming conditions.  She sets up a randomized block experiment with the three major types of soil in the region – sand, clay, and loam – as the blocks.  She selects a field with each soil type, divides it into four sections, and randomly selects one of the four wheat varieties for planting in each section.  The yields in bushels per acre in each section are shown in the following table. Variety Block A B C D Total Sand 20 21 21 18 80 Clay 25 24 21 20 90 Loam 30 28 22 20 100 Total 75 73 64 58 270 What are the degrees of freedom for total, treatments (i.e., varieties), blocks (i.e., soil types) and error for this randomized block experiment?

The partially completed ANOVA table for a 3 x 4 factorial experiment (i.e., there are 3 levels of factor A and 4 levels of factor B) with two replications is shown below: Source          df          SS          MS          F    Total                          18.1 Factor A                     0.8 Factor B                     5.3 A x B                           9.6 Error                                                                 Find the error sums of squares.

Find the probability of an observation lying more than z = 0.5 standard deviations below the mean.

Toyota would like to know how many miles per gallon the average driver gets when driving the hybrid Toyota Prius.  A random sample of 225 drivers yields a mean of 50 mpg and a standard deviation of 7.5 mpg. Estimate the population mean for the miles per gallon of the Prius using a 90% confidence interval.

Assume that 15% of all pigs die between birth and weaning.  In a random sample of 200 births, let X be the number of pigs that die between birth and weaning.  Using the normal approximation to the binomial, find the approximate probability that the number of pigs in the sample of 200 that die between birth and weaning is greater than or equal to 40.

The mean length of time required to complete a 5K race was 20 minutes.  The standard deviation of the times was 4 minutes.  The racing times were approximately normally distributed.  Only 10% of the runners would be expected to complete the race in less than x minutes.  Find the value of x.

A survey was conducted to determine how people rate the quality of programming available on TV.  Twenty-one respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display based on these data (using the first digit as the stem and the second digit as the leaf) is shown below: Stem                       Leaves                                     3               2     5 4               0     3     4     7     8     9 5               1     1     2     3     4     5 6               1     2     5     6     7 7               7     8 Based on the stem-and-leaf display, the median for these TV ratings is __________.

Find the probability of an observation lying more than z = 2.17 standard deviations above the mean.

A randomized block design is used to compare postweaning average daily gains of 4 breeds of beef cattle, Hereford, Angus, Charolais, and Simmental (we can think of the breeds at the “treatments”).  The breeds are divided into 3 weight classes (i.e., 3 blocks).  Block 1 contains cattle weighing 450 to 500 lb at the beginning of the experiment, block 2 contains cattle weighing 500 to 550 lb at the beginning of the experiment, and block 3 contains cattle weighing 550 to 600 lb at the beginning of the experiment.  The postweaning average daily gains (in pounds per day) are as follows:  Block Hereford Angus Charolais Simmental 1 3.50 3.60 3.70 3.75 2 3.55 3.63 3.71 3.80 3 3.56 3.62 3.80 3.90 The partially completed ANOVA table for this experiment is as follows: Source df SS MS F Total   .160     Breed   .139 .046 46 Block   .014 .007   Error   .007 .001   What are the correct degrees of freedom for total, breed, block, and error, respectively?