Question

A hungry, but very inquisitive student was taking a break from studying in the library. She went to the vending machine and bought a bag of Skittles. After returning to her table, she dumped them out on the table and noticed that her bag contained 25 red, 13 green, 17 yellow, 12 purple, and 24 orange candies. It seemed like an excess of red and orange and not enough purple or green. Do a χ² test to determine whether this is in fact a significant deviation from what she expected (an equal number of all colors).

1. How can we use Chi-squared analysis for the skittles problem?

- the dependent variable is continuous?

- The indpendent variable is discrete?

- both the dependent variable and the independent variable are continous

2. What is the expected number of red skittles in this problem?

3. What is the Chi-squared value for this question?

4. What is the degrees of freedom (df) for this problem?

5. What is the Pvalue?

6. What is the P value testing?

7. Should the hypthesis be rejected?

Answer 1

1. The independent variable discrete.

The Chi Square test is often used in science to determine if data you observe from an experiment is close enough to the predicted data. In genetics, for instance, you might expect to get a 75% to 25% ratio if you crossed two heterozygous tall plants (Tt x Tt). Calculating the X2 values help you determine whether the results follow the prediction and if the variations from the exact ratio are due to random chance. It's the question of "how close is close enough?" If the numbers differ greatly from your expected results, then it's possible that other factors may be influencing your results.

The Chi-square test is intended to test how likely it is that an observed distribution is due to chance. It is also called a "goodness of fit" statistic, because it measures how well the observed distribution of data fits with the distribution that is expected if the variables are independent.

2.The color proportions were calculated to be as follows: 22.3% purple, 21.6% orange, 21.0% yellow, 18.0% red, and 17.1% green. The reason that the Skittles candies were not exactly 20% for each color is because Skittles are packaged by machines and by weight, not by color.

The typical bag of Skittles contains 5 colors: Red, orange, yellow, green, and purple.

5. P-values are inherently linked to degrees of freedom; a lack of knowledge about degrees of freedom invariably leads to poor experimental design, mistaken statistical tests and awkward questions from peer reviewers or conference attendees.

If your test statistic is positive, first find the probability that Z is greater than your test statistic (look up your test statistic on the Z-table, find its corresponding probability, and subtract it from one). Then double this result to get the p-value.

6.Then double this probability to get the p-value. If your test statistic is positive, first find the probability that Z is greater than your test statistic (look up your test statistic on the Z-table, find its corresponding probability, and subtract it from one). Then double this result to get the p-value.

7. Hypothesis Test for a Mean

This lesson explains how to conduct a hypothesis test of a mean, when the following conditions are met:

The sampling method is simple random sampling.The sampling distribution is normal or nearly normal.

Generally, the sampling distribution will be approximately normally distributed if any of the following conditions apply.

The population distribution is normal.The population distribution is symmetric, unimodal, without outliers, and the sample size is 15 or less.The population distribution is moderately skewed, unimodal, without outliers, and the sample size is between 16 and 40.The sample size is greater than 40, without outliers.

This approach consists of four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results

.State the Hypotheses

Every hypothesis test requires the analyst to state a null hypothesis and an alternative hypothesis. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false; and vice versa.

The table below shows three sets of hypotheses. Each makes a statement about how the population mean μ is related to a specified value M. (In the table, the symbol ≠ means " not equal to ".)

The first set of hypotheses (Set 1) is an example of a two-tailed test, since an extreme value on either side of the sampling distribution would cause a researcher to reject the null hypothesis. The other two sets of hypotheses (Sets 2 and 3) are one-tailed tests, since an extreme value on only one side of the sampling distribution would cause a researcher to reject the null hypothesis.

Formulate an Analysis Plan

The analysis plan describes how to use sample data to accept or reject the null hypothesis. It should specify the following elements.

Significance level. Often, researchers choose significance levels equal to 0.01, 0.05, or 0.10; but any value between 0 and 1 can be used.Test method. Use the one-sample t-test to determine whether the hypothesized mean differs significantly from the observed sample mean.

4. Degree of freedom : The most commonly encountered equation to determine degrees of freedom in statistics is df = N-1. Use this number to look up the critical values for an equation using a critical value table, which in turn determines the statistical significance of the results.

For red = N-1 = 25 -1 = 24

For green = N-1 = 13 -1 = 12

For purple = N-1 = 12-1 = 11

For yellow= N-1 = 17- 1 = 16

For orange = N-1 = 24-1 = 23

3.To calculate chi square, take the square of the difference between the observed (o) and expected (e) values and divide it by the expected value. Depending on the number of categories of data, we may end up with two or more values. Remember that chi looks like the letter x, so that's the letter we use in the formula.

The chi square value of this question is 1671.

Thank You.