Use chi-square method **d)**Imagine that the calculated Chi Square statistic = 4.19. Calculate the *degrees of freedom* (show all your work!) and use an *alpha of .05* to determine whether or not the inferential statistic is statistically significant. Report the *critical value* you identify, and report the statistic in *APA style*:**e)***Summarize in words* what the descriptive and inferential statistics, and subsequent hypothesis testing, tell us about our original question (e.g., if there is a difference, where does it seem to be, is there a dependency, etc.): Certainly! Here's a detailed transcription and explanation appropriate for an educational website:---**Research Study on Clothing Preference by Time of Day****Introduction:**We conducted a study at night, right before a basketball game, and also collected data during the day. The goal was to determine if standing outside the SURC, there is an equal likelihood of seeing someone wearing a sweatshirt, long-sleeved shirt, or short-sleeved shirt, and if this distribution depends on the time of day.**a) Hypotheses:**- **Null Hypothesis (H₀):** The distribution of shirt types (sweatshirt, long-sleeved, short-sleeved) does not depend on the time of day. - **Alternative Hypothesis (H₁):** The distribution of shirt types depends on the time of day.**b) Data Collection and Analysis:**Both original and new data are presented in the table below, showing observed and expected frequencies for each shirt type during daytime and nighttime:| | Sweatshirt | Long Sleeved Shirt | Short Sleeved Shirt | Total ||----------------------|------------|--------------------|---------------------|-------|| **Day – Observed** | 13 | 14 | 9 | 36 || **Day – Expected** | 16.62 | 10.15 | 9.23 | || **Night – Observed** | 23 | 8 | 11 | 42 || **Night – Expected** | 19.38 | 11.85 | 10.77 | || **Total** | 36 | 22 | 20 | |**Key Observation:** The table compares the observed frequencies of each shirt type with the expected frequencies to determine if there is a significant difference that could indicate a dependency on the time of day.**Identify the Appropriate Statistical Test:**The appropriate inferential statistic to use here is the Chi-square test for independence. This test helps to determine if there is a significant relationship between the two categorical variables: shirt type and time of day.**c) Formula for the Inferential Statistic:**The formula for the Chi-square test is:\[ \chi^2 = \sum \frac{(O - E)^2}{E} \]Where:- \( O \) = Observed

Hi there! Thank you for the question. As per the honor code, we are allowed to answer three…

2) We conducted the previous study at night, right before a basketball game. We also collect data during the day. Using the extra data collected, we want to attempt to again identify if standing outside of the SURC, you are equally likely to see someone wearing a sweatshirt, long sleeved shirt, or short sleeved shirt, and if that distribution depends on the time of day. a) Describe the null and alternative hypotheses (hint: do not use directional hypotheses): b) The original data along with the newly collected data are presented in the following table. Day-Observed Day-Expected Night-Observed Night-Expected Total Sweatshirt 13 16.62 23 19.38 36 Long sleeved Short sleeved shirt 14 10.15 8 11.85 22 shirt 9 9.23 11 10.77 20 Total 36 42 Identify the appropriate inferential statistic and test needed to answer our research question. c) What is the formula for the appropriate inferential statistic needed to answer our research question?