Student 1
Hello, typically, it is expected that there is an association between gender and color preference, that is, women prefer the blue color while men like brown. As such, for the one hundred fashion designers, it would be observed that there will be a high correlation between gender and color preference. According to Statistics How To (2019), a low value for chi-square implies that there is a great correlation between two sets of data. Therefore, the chi-square test, in this case, is expected to have a small value. A chi-squared statistic is a distinct number, which tells one how much difference subsists between the observed and expected counts if no relationship exists at all in a population (Statistics How To, 2019) . Typically, to test a h ypothesis for the chi-square test of independence, a test statistic is calculated and compared to a critical value (Statistics Solutions, 2019). If the experiential chi-square test statistic is larger than the critical value, the null hypothesis would be rejected; thus, the alternative hypothesis accepted (Statistics Solutions, 2019). In this case, we shall accept the alternative hypothesis holding that there is a significant association between gender and either blue or brown colors.
References
Statistics How To. (2019). Chi-Square Statistic: How to Calculate It / Distribution -. Retrieved 20 July 2019, from https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/chi-square/
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Statistics Solutions. (2019). Chi-Square Test of Independence. Retrieved 20 July 2019, from https://www.statisticssolutions.com/non-parametric-analysis-chi-square/
Student 2
Hello, t-tests are convenient hypothesis tests in statistics, especially when one wants to compare means (Minitab, LLC, 2016). The null hypothesis for independent samples in t-test assumes that the means are equal. Usually, t -test allows one to answer the query, are these two sets statistically different from each other? Therefore, the null hypothesis will show that there is no statistical difference between the means of the two sets. Hence, upon rejecting the null hypothesis when using a t-test, it is evident that the means would be statistically different (Minitab, LLC, 2016). In this case, the means of the samples will be taken and the null hypothesis, which will be rejected, will be that there is no statistical difference between the means of color preferences between men and women. Regarding the null hypothesis in ANOVA, no difference exists in the sample means ( Sullivan, n.d.). However, the alternative hypothesis includes any difference in means and comprises, for instance, the case where all 4 means are unequal, where 1 is different from the other 3, and where 2 are different ( Sullivan, n.d.). The hypotheses can be represented as H 0 : μ 1 = μ 2 = μ 3 = μ 4 and H 1 : The means are not all equal.
References
Minitab, LLC. (2016). Understanding t-Tests: t-values and t-distributions. Retrieved 20 July 2019, from https://blog.minitab.com/blog/adventures-in-statistics-2/understanding-t-tests-t-values-and-t-distributions
Sullivan, L. (n.d.). Hypothesis Testing - Analysis of Variance (ANOVA). Retrieved 20 July 2019, from http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_HypothesisTesting-ANOVA/BS704_HypothesisTesting-Anova_print.html
