Please show how to solev ### Analysis of Birthday Distribution by Season**Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others?** This was the question posed by the owners of a children's toy store chain. The data collected by the chain are summarized in the table below.The data were obtained from a random sample of 190 people. Each person's birthdate was recorded and categorized into one of four seasons:- **Winter (December 21 - March 20)**- **Spring (March 21 - June 20)**- **Summer (June 21 - September 20)**- **Fall (September 21 - December 20)**The top row of the table provides the observed frequencies of birthdays in these seasons. The expected frequencies for each season are calculated under the assumption that birthdays are equally likely during each season of the year.#### Formula for Calculating Chi-Square ValueThe chi-square value is calculated using the formula:\[\chi^2 = \sum \frac{(f_O - f_E)^2}{f_E}\]where:- \( f_O \) is the observed frequency- \( f_E \) is the expected frequency### Part 1: Data Analysis TableFill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. Round your chi-square values to three or more decimal places.| Season | Observed Frequency (\( f_O \)) | Expected Frequency (\( f_E \)) | \(\frac{(f_O - f_E)^2}{f_E}\) ||----------|-------------------------------|-------------------------------|-------------------------------|| Winter | 39 | 47.50 | 1.521 || Spring | 39 | 47.50 | || Summer | 52 | | || Fall | 60 | 47.50 | 3.289 || **Total** | **190** | | |### Part 2: Check Your WorkClick the "Check" button to verify your answers.---**Interaction Tools:**- **Explanation**: Provides detailed steps on how to calculate each value- **Check**: Verifies your entered values against the correct answersBy understanding the distribution of birthdays across seasons, the toy store can ### Analysis of Birthdates Across SeasonsThis educational section will guide you through the statistical process to determine if birthdays are equally likely during each season of the year. The analysis is done using observed and expected frequencies to test the hypothesis.#### Table of Observed and Expected Frequencies| | Winter | Spring | Summer | Fall | Total ||------------|--------|--------|--------|------|-------|| **Observed frequency (f_o)** | 39 | 39 | 52 | 60 | 190 || **Expected frequency (f_e)** | | 47.50 | | 47.50| || **\(\frac{(f_o - f_e)^2}{f_e}\)** | | 1.521 | | 3.289| |### Part 2: Hypothesis TestingAnswer the following prompts to summarize the test of the hypothesis that birthdays are equally likely during each season of the year. Use the 0.10 level of significance for the test.1. **Determine the type of test statistic to use.** - **Type of test statistic:** ```(Choose one)```2. **Find the value of the test statistic.** - **Value of the test statistic:** ```(Round your answer to two or more decimal places.)```3. **Find the p-value.** - **p-value:** ```(Round your answer to three or more decimal places.)```4. **Can we reject the hypothesis that birthdays are equally likely during each season of the year?** - ```Yes``` - ```No``` ### Explanation of the TableThe table lists the observed frequencies (the actual number of births recorded) for each season: Winter, Spring, Summer, and Fall. It also shows the expected frequencies, which are the average number of births we would expect if birthdays were equally likely in any season.The third row of the table calculates each cell's chi-square component. This is done by taking the difference between observed and expected frequencies, squaring it, and then dividing by the expected frequency.#### Steps to Complete:1. **Determine the type of test statistic:** This will typically be a chi-square test for independence.2. **Calculate the test statistic:** Sum the chi-square components \(\frac{(f_o - f_e)^

The chi-squared estimate is a single figure that indicates the level to which the scores we…

Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others? Owners of a children's toy store chain asked this question. Some data collected by the chain are summarized in the table below. The data were obtained from a random sample of 190 people. The birthdate of each person was recorded, and each of these dates was placed into one of four categories: winter (December 21-March 20), spring (March 21-June 20), summer (June 21-September 20), and fall (September 21-December 20). The numbers in the first row of the table are the frequencies observed in the sample for these season categories. The numbers in the second row are the expected frequencies under the assumption that birthdays are equally likely during each season of the year. The bottom row of numbers gives the following value for each of the season categories. (fo-JB)² ƒE Part 1 Fill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. Round your three or more decimal places. Send data to Excel Observed frequency fo Expected frequency SE (Observed frequency - Expected frequency)² Expected frequency (Jo-JE)² fr Winter 39 0 0 Spring a 39 47.50 1.521 Summer 52 0 0 Fall 60 47.50 3.289 Total 190 X S ? (fo-fB)² ƒE responses to Espai C E E

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P