A table classifying a random sample of students by course and whether or not they are "binge drinkers" is given below.Science (BSc, BBiomed, BEng) Arts (BA, BMusic) Total"binge drinker" 68 63 131not "binge drinker" 355 423 778Total 423 486 909When testing the null hypothesis that there is no association between gender and "binge drinking",  which ONE of the following statements is FALSE?Group of answer choicesThe assumptions for the chi-squared test are invalid.A suitable test statistic has a value of 1.33A suitable test statistic has a value of 1.776The p-value for the test is 0.183Based on this data, there is insufficient evidence to suggest that science students are more likely than arts students to be "binge drinkers".

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.

In the chi-square test, the null hypothesis states:a.There is an association between the variablesb.There is no association between the variablesc.The means of the groups are equald.The variances of the groups are equal

The following table shows results from a general survey conducted by a dating web site from a random sample of 100 people on the type of dating activity and whether a person's enjoyed their date.Results of Date Type of Activity Good Date Bad Date Neutral Row TotalIndoor Activity 21 23 9 53Outdoor Activity 30 12 5 47Column Total 51 35 14 100Use the chi-square test to determine that the type of dating activity and results of a date are independent at the 0.05 level of significance.(a)What is the level of significance? State the null and alternate hypotheses.H0: The type of dating activity and date results are independent.H1: The type of dating activity and date results are not independent.H0: The type of dating activity and date results are not independent.H1: The type of dating activity and date results are not independent.    H0: The type of dating activity and date results are independent.H1: The type of dating activity and date results are independent.H0: The type of dating activity and date results are not independent.H1: The type of dating activity and date results are independent.(b)Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)Are all the expected frequencies greater than 5?YesNo    What sampling distribution will you use?binomialStudent's t    chi-squarenormaluniformWhat are the degrees of freedom? (c)Find or estimate the P-value of the sample test statistic.P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005(d)Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?Since the P-value > 𝛼, we reject the null hypothesis.Since the P-value ≤ 𝛼, we reject the null hypothesis.    Since the P-value > 𝛼, we fail to reject the null hypothesis.Since the P-value ≤ 𝛼, we fail to reject the null hypothesis.(e)Interpret your conclusion in the context of the application.At the 5% level of significance, there is sufficient evidence to conclude that the type of dating activity and results of a date are not independent.At the 5% level of significance, there is insufficient evidence to conclude that the type of dating activity and results of a date are not independent.

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

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)