QUAN102: Statistics for Business assignment sample NZ

Statistical analysis is an important tool for making informed business decisions. In this assignment, you will use statistics to analyze data from a survey of college students. You will then use your findings to make recommendations for improving the quality of education at your school.

In business, statistics can be used to measure performance, forecast future trends, and determine risk.

There are a variety of different types of statistical analyses that can be useful for business purposes. Some common ones include:

1. Descriptive statistics, which summarize data in a way that makes it easy to understand
2. Inferential statistics, which allow you to make predictions about populations based on information from samples
3. Time series analysis, which allows you to track changes in data over time
4. Regression analysis, which helps you understand the relationships between different variables
5. Correlation analysis, which measures the strength of the relationship between two variables
6. Experimental design, which helps you understand the impact of factors like price and promotion on consumer buying behavior.

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This course will increase your students’ knowledge and understanding of the subject. The following are some tasks that will be answered in this course:

Assignment Tasks 1: Process data, using simple graphical techniques.

There are a variety of different graphical techniques that can be used to process data. The most common is the bar chart, which is used to compare different groups of data.

Another common technique is the line graph, which is used to track changes in data over time. This can be especially useful for tracking changes in things like stock prices or weather patterns.

Finally, histograms can be used to show the distribution of data points within a particular group. This can be helpful for understanding things like income distribution or voter turnout.

There are also several statistical tests that can be used to process data. These include:

• The mean, which is useful for understanding the middle point of a dataset
• The median, which may be more accurate when there is an outlier or trend within the data set
• The mode, which is the most common value in the data set
• The range, which is useful for understanding the spread of data points
• The standard deviation, which measures how far from the average value a particular point falls.

Assignment Task 2: Evaluate for univariate data a range of sample statistics, including mean, standard deviation, and percentiles.

Mean, standard deviation, and percentiles are all measures of central tendency and variability. The mean is the most common measure of central tendency, and it's calculated by adding up all the data points and dividing by the number of data points. The standard deviation is a measure of variability, and it's calculated by taking the square root of the variance. The variance is calculated by taking the difference between each data point and the mean, squaring them, then dividing by the number of data points minus 1. Finally, percentiles are a way to rank data in order from smallest to largest.

For example, if you wanted to know what percentile rank a score falls into for a given set of data, you would find the score that falls into the top 100%, then the score that falls into the bottom 99% (e.g., if you have 500 scores in your data, you would find the percentiles for the 500th and 501st scores).

Assignment Task 3: Evaluate and interpret a linear relationship between two variables.

When evaluating a linear relationship between two variables, it's important to first determine whether the data points fit a straight line. This can be done by plotting the data points and eyeballing whether they appear to form a straight line. If they do, then you can use a mathematical equation to determine the slope and y-intercept of the line.

The slope of a line is determined by calculating the change in y-value divided by the change in x-value for each point on the line. The y-intercept is determined by setting x=0 and solving for y. Once you have the slope and y-intercept, you can use them to graph a best-fit line through the data points.

Plotting data points can be time-consuming, so many students will use a graphing calculator to do the calculations for them. A Google search of "free online graphing calculator" will yield several websites with equations that can be copied and pasted into your graphing calculators directly.

Assignment Task 4: Use basic rules of probability to solve problems with up to three stages.

There are many different ways to solve probability problems, but here is one approach that can be used for problems with up to three stages.

1. Draw a diagram that shows all the possible outcomes for the problem.
2. Assign a probability to each outcome.
3. Multiply the probabilities of all the outcomes in the first stage together to find the probability of that stage happening.

Here is an example problem: A fair coin is flipped three times. What is the probability of getting heads on two of the flips?

The possible outcomes are HH, HT, TH, and TT. The probability of getting heads on two of the flips is the probability of HH * probability of HT * probability of TH = (1/2) * (1/2) * (1/2) = 1/8.

You can refer to this table for some probabilities you might want to memorize:

A more efficient approach, however, is to learn the patterns that occur when multiplying probabilities. To determine the probability of HH, for example, you need to count the number of ways to get heads by multiplying 1/2 by itself three times: 1/2 * 1/2 * 1/2 = 1/8. This pattern will work on any three coin flips and is memorized as the combinations formula: n! / (k! * (n-k)!), where "n" is the number of things and "k" is the number you want. For this problem, k = 2 and n = 3. There are six possible outcomes for three coin flips.

Assignment Task 5: Obtain probabilities from the binomial and normal distributions.

The binomial distribution gives the probability of obtaining a certain number of successes out of a fixed number of trials, while the normal distribution gives the probability of obtaining any particular value given a certain deviation from the mean.

For example, if you want to find the probability that a random person selected at random has a blood pressure between 120 and 130 mmHg, you would use the normal distribution. Or, if you wanted to find the probability that a person chosen at random will have exactly 4 successes in 10 trials, you would use the binomial distribution.

Assignment Task 6: State the central limit theorem, and discuss its applicability.

The Central Limit Theorem states that the distribution of a sum of independent random variables will be approximately normal, regardless of the shape of the individual distributions. This theorem is particularly useful in statistics, as it allows for the calculation of probabilities for events occurring as a result of sums of random variables.

This theorem is highly applicable in many real-world situations, such as when calculating sampling error or confidence intervals. Additionally, the Central Limit Theorem can also be used to model financial markets and other complex systems.

Assignment Task 7: Implement a range of hypothesis tests, and use these to draw conclusions about population parameters from sample data.

Hypothesis tests are used to determine the likelihood that a population parameter is equal to a certain value. This can be done by sampling data from the population and calculating the corresponding test statistic. If this test statistic falls within the boundaries of the appropriate critical region, then we can conclude that the null hypothesis is likely to be true. Alternately, if the test statistic does not fall within these boundaries, then we can reject the null hypothesis and conclude that there is a statistically significant difference between the population parameter and the hypothesized value.

Here is an example of how to use a t-test: Assuming that the average height for adult women in the US is 64 inches, we can take a random sample from this population and calculate the mean height. We will then use a T-distribution table to determine the critical value necessary for our desired significance level (alpha). This critical value will be a function of the degrees of freedom and will tell us how far from the mean we can expect our test statistic to fall. If our test statistic falls within the boundaries of this critical region, then we can conclude that there is not a statistically significant difference between the population parameter and 64 inches. In other words, the null hypothesis cannot be rejected.

Assignment Task 8: Form confidence intervals for a range of population parameters, and interpret these intervals.

A confidence interval gives an estimated range of values for a population parameter. It is computed by estimating the value of the population parameter and then constructing a confidence interval around that estimate. The width of the confidence interval depends on the level of confidence selected (usually 95% or 99%), and on the sample size.

The interpretation of a confidence interval is that if we were to select repeated samples from the population, 95% (or 99%, depending on the level of confidence) of those intervals would contain the true value for the population parameter. So, we can say that there is a 95% (or 99%) chance that the true value for the population parameter lies within the given range.

Assignment Task 9: Interpret the output of statistical software for advanced hypothesis tests via p-values.

When carrying out a hypothesis test, the first step is to calculate a p-value. This is a measure of how likely it is that the results of the study could have occurred by chance. If the p-value is less than 0.05, this indicates that there is less than a 5% chance of the results having occurred by chance and thus you can reject the null hypothesis.

A high p-value does not mean that you can accept the null hypothesis, it only means that there is a greater than 95% chance that the results occurred by chance. It's important to remember this when interpreting statistical results.

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