Testing for One-Proportion and Chi-Square Goodness of Fit

Testing for One-Proportion and Chi-Square Goodness of Fit

Introduction:

In this section, we use the well-known iris dataset to perform a one-proportion test and a chi-square goodness of fit test. The dataset contains information about the sepal length, sepal width, petal length, petal width, species, and size (small or big) of 150 flowers.

Using the prop.test() function, we test whether the proportion of small flowers is different from the proportion of big flowers. The null hypothesis is that the proportions are equal, and the alternative hypothesis is that they are different. The test results show that the p-value is 0.8065, indicating that we do not reject the null hypothesis at a 5% significance level.

Next, we perform a chi-square goodness of fit test to determine whether the three species (setosa, versicolor, and virginica) are equally common. The null hypothesis is that the proportions of each species are equal. The test results show a p-value of 1, suggesting that we do not reject the null hypothesis.

These tests provide insights into the distribution and proportions of small and big flowers, as well as the distribution of species within the dataset.

Full Article: Testing for One-Proportion and Chi-Square Goodness of Fit

Data Analysis on Flower Sizes: Using the Iris Dataset

In this news report, we will be analyzing the size of flowers using the well-known iris dataset. The dataset includes information on various attributes of different flowers, including their size. We will be conducting one-proportion and chi-square tests to determine if there are any significant differences in the proportions of different flower sizes.

One-Proportion Test

We will begin by conducting a one-proportion test to compare the proportions of small and big flowers within our sample. Out of the 150 flowers in our sample, 77 are categorized as big, while 73 are categorized as small. This translates to proportions of 51% and 49% respectively.

To test if these proportions are significantly different, we will use the prop.test() function. The null hypothesis (H0) states that the proportions of big and small flowers are equal, while the alternative hypothesis (H1) states that the proportions are different.

The results of the test indicate that the test statistic is 0.06, with 1 degree of freedom and a p-value of 0.8065. With a significance level of 5%, we do not have enough evidence to reject the null hypothesis. Therefore, we conclude that there is no significant difference in the proportions of big and small flowers.

Assumption of prop.test() and binom.test()

It is important to note that prop.test() assumes a normal approximation to the binomial distribution. One of the assumptions of this test is that the sample size is large enough, usually exceeding 30. If the sample size is smaller, it is recommended to use the exact binomial test, which can be performed using the binom.test() function.

Chi-Square Goodness of Fit Test

Next, we will conduct a chi-square goodness of fit test to analyze the proportions of different flower species. The variable “Species” has three levels: setosa, versicolor, and virginica. Each species has precisely 50 observations.

The null hypothesis (H0) states that the proportions of each species are equal, while the alternative hypothesis (H1) states that at least one species has a different proportion.

Using the chisq.test() function, we find that the test statistic is 0, with 2 degrees of freedom and a p-value of 1. With a significance level of 5%, we do not have enough evidence to reject the null hypothesis. Therefore, we conclude that the proportions of the three flower species are equal.

Conclusion

In conclusion, our analysis of the iris dataset using one-proportion and chi-square tests did not find any significant differences in the proportions of big and small flowers or among the different flower species. These findings suggest that the sizes and distributions of flowers in the given sample are relatively equal.

Summary: Testing for One-Proportion and Chi-Square Goodness of Fit

In this section, we use the same dataset as the article on descriptive statistics, which is the well-known iris dataset. We add a variable called “size” which categorizes the flowers as small or big based on the length of the petal. We then perform a one-proportion test to compare the proportions of small and big flowers in the sample. The results of the test show that the proportions are not significantly different. We also discuss the assumptions of the prop.test() function and mention the alternative binom.test() function for small sample sizes. Additionally, we demonstrate a chi-square goodness of fit test to examine the proportions of different species in the dataset. The test confirms that the species are equally common.

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