Chicken farming is a multi-billion dollar industry, and any methods that increase the growth rate of young chicks can reduce consumer costs while increasing company profits, possibly by millions of dollars. An experiment was conducted to measure and compare the effectiveness of various feed supplements on the growth rate of chickens. Newly hatched chicks were randomly allocated into six groups, and each group was given a different feed supplement. Below are some summary statistics from this data set showing the distribution of weights by feed type. Mean SD Sample Size casein 323.58 64.43 12 horsebean 160.20 38.63 10 linseed 218.75 52.24 12 meatmeal 276.91 64.90 11 soybean 246.43 54.13 14 sunflower 328.92 48.84 12 (a) Do these data provide strong evidence that the average weights of chickens that were fed lineseed and horsebean are different? Use a 5% significance level. Hint: We are interested in the difference: lineseed-horsebean Test Statistic: _______ P-Value:_______ (b) Do these data provide strong evidence that the average weights of chickens that were fed lineseed and sunflower are different? Use a 5% significance level. Hint: We are interested in the difference: lineseed-sunflower Test Statistic = _________ p-value = ________ (c) Create a 99% confidence interval for the difference between the means of meatmeal and soybean. Hint: We are interested in the difference: meatmeal-soybean Lower Bound = ________ Upper Bound = ________
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Chicken farming is a multi-billion dollar industry, and any methods that increase the growth rate of young chicks can reduce consumer costs while increasing company profits, possibly by millions of dollars. An experiment was conducted to measure and compare the effectiveness of various feed supplements on the growth rate of chickens. Newly hatched chicks were randomly allocated into six groups, and each group was given a different feed supplement. Below are some summary statistics from this data set showing the distribution of weights by feed type.
| Mean | SD | ||
| casein | 323.58 | 64.43 | 12 |
| horsebean | 160.20 | 38.63 | 10 |
| linseed | 218.75 | 52.24 | 12 |
| meatmeal | 276.91 | 64.90 | 11 |
| soybean | 246.43 | 54.13 | 14 |
| sunflower | 328.92 | 48.84 | 12 |
(a) Do these data provide strong evidence that the average weights of chickens that were fed lineseed and horsebean are different? Use a 5% significance level.
Hint: We are interested in the difference: lineseed-horsebean
Test Statistic: _______
P-Value:_______
(b) Do these data provide strong evidence that the average weights of chickens that were fed lineseed and sunflower are different? Use a 5% significance level.
Hint: We are interested in the difference: lineseed-sunflower
Test Statistic = _________
p-value = ________
(c) Create a 99% confidence interval for the difference between the means of meatmeal and soybean.
Hint: We are interested in the difference: meatmeal-soybean
Lower Bound = ________
Upper Bound = ________
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