1. Draw a simple random sample of 15 students from your class, and calculate sample mean and sample variance of their heights(use Lottery method )
2. Three blocks of Coal were analyzed by Four Chemists and the ash-content in the blocks was found to be as under:
Chemists
Blocks I II III IV
A 18 15 15 17
B 17 16 14 14
C 13 16 15 14
Do the blocks differ in their ash-content? Do the chemists differ significantly their analysis?
In the above examples, identify the following.
i. Experiment
ii. Experimental unit
iii. Treatments
iv. Varieties/blocks
v. Experimental error
vi. Yield
vii. Replication
viii. Randomization
ix. Local control if any
3. Collect the annual sales of a Super market for 10 years and fit a straight line Trend to the data collected and find the trend values.
4. Explain laws of supply and demand by taking at least 1 item for each type of commodity
Please only post your questions once. Repeating posts will not get a quicker response. In addition, it wastes our time looking over reposts that have already been answered in another post. Thank you.
I answered #1 in your previous post.
2. Use a 3 by 4 X^2 (Chi-Square) test.
http://www.google.com/search?client=safari&rls=en&q=chi+square+test&ie=UTF-8&oe=UTF-8
Without the data, we cannot respond to #3 or 4.
Lastly, we do not do your work for you. Once you have attempted to answer your questions, we will be happy to give you feedback on your work. Although it might require more time and effort, you will learn more if you do your own work. Isn't that why you go to school?
1. To draw a simple random sample of 15 students from your class and calculate the sample mean and sample variance of their heights using the Lottery method, you can follow these steps:
Step 1: Assign a unique number to each student in your class.
Step 2: Write down all the assigned numbers on separate pieces of paper and put them in a container (e.g., a hat).
Step 3: Thoroughly mix the pieces of paper in the container to ensure randomness.
Step 4: Close your eyes and pick out 15 pieces of paper, one at a time, from the container. This represents your simple random sample of 15 students.
Step 5: Record the heights of the selected students.
Step 6: Calculate the sample mean by summing up all the heights and dividing the sum by 15 (the sample size).
Step 7: Calculate the sample variance by taking the sum of squared deviations from the sample mean divided by (n-1), where n is the sample size.
Remember, the Lottery method ensures that each student in your class has an equal chance of being selected, providing a randomly representative sample.
2. Let's identify the different components in the given example:
i. Experiment: The analysis of the ash content in the coal blocks by the chemists.
ii. Experimental unit: The coal blocks.
iii. Treatments: The different chemists' analysis of the ash content (A, B, C).
iv. Varieties/blocks: The three coal blocks (I, II, III).
v. Experimental error: Variability in the measurements or differences between actual and expected values.
vi. Yield: In this example, yield is not explicitly mentioned. It could refer to the percentage of ash content in the coal blocks.
vii. Replication: There is no replication mentioned in the example; each block is analyzed once by each chemist.
viii. Randomization: The assignment of the coal blocks to the chemists' analysis should ideally be randomized to reduce bias.
ix. Local control: There is no local control specified in the example.
3. To collect the annual sales of a supermarket for 10 years and fit a straight line Trend to the data collected to find the trend values, you can follow these steps:
Step 1: Gather the annual sales data for the supermarket for each of the 10 years.
Step 2: Plot the data points on a graph with the years on the x-axis and the corresponding sales on the y-axis.
Step 3: Analyze the pattern of the data. If there appears to be a linear relationship between the years and sales, you can proceed to fit a straight line trend.
Step 4: Use a regression analysis technique, such as linear regression, to find the equation of the straight line that best fits the data. The equation will be in the form of y = mx + c, where y represents the sales, x represents the years, m represents the slope, and c represents the intercept.
Step 5: Once you have the equation of the line, you can use it to predict the trend values for any future years or make other relevant analyses.
4. The laws of supply and demand explain the relationship between the availability of a commodity (supply) and the desire or demand for that commodity. Here's an explanation using an example of two different commodities:
i. Commodity: Apples
- Law of Supply: The law of supply states that, all else being equal, the quantity of apples that producers are willing to supply will increase as the price of apples increases. In other words, as the price of apples goes up, producers are motivated to supply more apples to the market.
- Law of Demand: The law of demand states that, all else being equal, the quantity of apples that consumers are willing to purchase will decrease as the price of apples increases. In other words, as the price of apples goes up, consumers tend to demand less, reducing the quantity sold.
ii. Commodity: Cell Phones
- Law of Supply: The law of supply states that, all else being equal, the quantity of cell phones that producers are willing to supply will increase as the price of cell phones increases. As the price of cell phones rises, manufacturers expand production to take advantage of the higher profit margins.
- Law of Demand: The law of demand states that, all else being equal, the quantity of cell phones that consumers are willing to purchase will decrease as the price of cell phones increases. As the price of cell phones goes up, consumers may either delay their purchases or choose lower-priced alternatives, resulting in reduced demand.
In both cases, the laws of supply and demand interact to influence the market equilibrium, where the supply and demand curves intersect to determine the price and quantity traded in the market. When the supply and demand are in balance, there is an equilibrium price and quantity that maximize overall trade and welfare.