A necessary assumption that is made when conducting a chi-squared analysis is: (select the one false statement)Group of answer choicesat least 80% of the observed frequencies are greater than or equal to 5all expected frequencies are greater than or equal to 1the sample size is large enough to approximate a Binomial random variable by a normal random variablethe sample data consist of frequency counts for different categories of a tablea subject can only fit into one category of the table (i.e. they belong with only one cell of the table)

Which of the following statements about the Chi-square analysis is true? Categorical data from questions about sex, education, or other nominal variables cannot be tested with this statistic. The expected frequencies in Chi-square cannot be calculated theoretically. The larger the Chi-square, the less likely it is that the two variables that are measured are related. When the differences between observed and expected frequencies are large, one must accept the null hypothesis. Chi-square analysis compares the observed frequencies of responses with the expected frequencies.

Chi-square analysis enables researchers to test for statistical significance between the frequency distributions of two or more nominally scaled variables in a cross-tabulation table to determine if there is any association between the variables. True False

To calculate the chi-squared statistic, we need to follow these steps: ### Step-by-Step Calculation: #### iii) Calculate the Expected FrequenciesThe expected frequency for each cell in a contingency table is calculated using the formula: \[ E_{ij} = \frac{( \text{Row Total}_i \times \text{Column Total}_j )}{\text{Grand Total}} \] Let's calculate the expected frequencies for each cell: 1. **Facebook:** - Female: \( E_{11} = \frac{(117 \times 64)}{249} \approx 30.07 \) - Male: \( E_{12} = \frac{(132 \times 64)}{249} \approx 33.93 \) 2. **Instagram:** - Female: \( E_{21} = \frac{(117 \times 64)}{249} \approx 30.07 \) - Male: \( E_{22} = \frac{(132 \times 64)}{249} \approx 33.93 \) 3. **Snapchat:** - Female: \( E_{31} = \frac{(117 \times 58)}{249} \approx 27.25 \) - Male: \( E_{32} = \frac{(132 \times 58)}{249} \approx 30.75 \) 4. **Twitter:** - Female: \( E_{41} = \frac{(117 \times 63)}{249} \approx 29.6 \) - Male: \( E_{42} = \frac{(132 \times 63)}{249} \approx 33.4 \) The expected frequencies are: | | Facebook | Instagram | Snapchat | Twitter | Row Total | |------------|----------|-----------|----------|---------|-----------| | **Female** | 30.07 | 30.07 | 27.25 | 29.6 | 117 | | **Male** | 33.93 | 33.93 | 30.75 | 33.4 | 132 | | **Column Total** | 64 | 64 | 58 | 63 | 249 | #### iv) Calculate the Chi-Squared StatisticThe chi-squared statistic is calculated using the formula: \[ \chi^2 = \sum \frac{(O_{ij} - E_{ij})^2}{E_{ij}} \] Where \( O_{ij} \) is the observed frequency and \( E_{ij} \) is the expected frequency. Let's calculate the chi-squared statistic step by step: 1. **Facebook:** - Female: \( \frac{(33 - 30.07)^2}{30.07} \approx 0.29 \) - Male: \( \frac{(31 - 33.93)^2}{33.93} \approx 0.25 \) 2. **Instagram:** - Female: \( \frac{(30 - 30.07)^2}{30.07} \approx 0.00 \) - Male: \( \frac{(34 - 33.93)^2}{33.93} \approx 0.00 \) 3. **Snapchat:** - Female: \( \frac{(26 - 27.25)^2}{27.25} \approx 0.06 \) - Male: \( \frac{(32 - 30.75)^2}{30.75} \approx 0.05 \) 4. **Twitter:** - Female: \( \frac{(28 - 29.6)^2}{29.6} \approx 0.09 \) - Male: \( \frac{(35 - 33.4)^2}{33.4} \approx 0.08 \) Summing these values: \[ \chi^2 = 0.29 + 0.25 + 0.00 + 0.00 + 0.06 + 0.05 + 0.09 + 0.08 = 0.82 \] So, the chi-squared statistic is: \[ \chi^2 \approx 0.82 \] This value should be entered in the box for the chi-squared statistic.

What does a chi-square test compare?Question 4Answera.the frequency of incorrect responses for each variableb.correct and incorrect reaction timesc.the observed and total frequencies for each individual participantd.the observed and expected frequencies for each cell

For what type of data do we use a Chi-squared Test?Group of answer choicesQualitativeQuantitativeNormalBinomial