(1 point) Do less agreeable Facebook users tend to spend more time on Facebook? A study (Ivcevic and Ambady, 2013) aimed to investigate various facets of use of the social networking website Facebook. Previous research suggested that individuals with poorer face-to-face social skills may find internet-based social platforms less daunting, so as part of the study Ivcevic and Ambady investigated whether an individual's volume of Facebook use was associated with levels of "agreeableness". The subjects were 99 university students who all had a Facebook page. The subjects agreed to allowing the content of their Facebook pages to be downloaded on six separate occasions over a three-week period. As part of the data gathered on each subject, each of the 99 were individually rated by a selected friend on an "agreeableness" scale (based on average ratings on a questionnaire where all responses were on a Likert scale), with 1 being "low" and 5 "high". We consider here the relationship between "friend reported" agreeableness and the number of words the subjects posted on their Facebook pages per day, as measured by an average word count over a subset of the six days. Suppose the data were as illustrated below: FaceBook Activity against Friend-reported Agreeableness Rating OO O Daily no. of words on FaceBook entries O oo O O o C 0 6 O 2.5 3.0 3.5 4.0 4.5 5.0 Friend-reported agreeableness Ivcevic, Z. and Ambady, N. (2013): Face to (Face)Book: The two faces of social behaviour? Journal of Personality 8 No.3, 290-300.Part a) Which of the following is most likely to be the correlation between the two variables above? O A. 0.5 O B. -0.9 O C. -0.3 O D. -0.05 O E. O Part b) If a linear model is fitted to the data above by least squares, the estimate of the slope parameter is -12.503 and the estimate of the intercept is 73.336. The standard error of the estimate of the slope coefficient was found to be 2.032. Provide a 95% confidence interval for the underlying slope parameter, giving your bounds to 3 decimal places. Lower bound: Upper bound: Part c) If testing the null hypothesis that the volume of FaceBook activity (as measured by mean daily word counts on updates) does not depend linearly on agreeableness, what would be your test statistic (to 3 decimal places)?Part d) Assuming the test is at the 5% significance level, what would you conclude from the above hypothesis test? A. Since the observed test statistic does not fall in either the upper or lower 5 percentiles of the t distribution with 97 degrees of freedom, we cannot reject the null hypothesis that the volume of FaceBook activity does not depend linearly on agreeableness. B. Since the observed test statistic falls in the lower 5 percentile of the t distribution with 97 degrees of freedom, we can reject the null hypothesis that the volume of FaceBook activity does not depend linearly on agreeableness. C. Since the observed test statistic falls in the lower 5 percentile of the t distribution with 97 degrees of freedom, we cannot reject the null hypothesis that the volume of FaceBook activity does not depend linearly on agreeableness. D. Since the observed test statistic does not fall in the lower 5 percentile of the t distribution with 97 degrees of freedom, we cannot reject the null hypothesis that the volume of FaceBook activity does not depend linearly on agreeableness. O E. Since the observed test statistic falls in either the upper or lower 2- percentiles of the t distribution with 97 degrees of freedom, we cannot reject the null hypothesis that the volume of FaceBook activity does not depend linearly on agreeableness. F. Since the observed test statistic falls in either the upper or lower 2 - percentiles of the t distribution with 97 degrees of freedom, we can reject the null hypothesis that the volume of FaceBook activity does not depend linearly on agreeableness. O G. Since the observed test statistic does not fall in either the upper or lower 2, percentiles of the t distribution with 97 degrees of freedom, we cannot reject the null hypothesis that the volume of FaceBook activity does not depend linearly on agreeableness. O H. Since the observed test statistic does not fall in either the upper or lower 2- percentiles of the t distribution with 97 degrees of freedom, we can reject the null hypothesis that the volume of FaceBook activity does not depend linearly on agreeableness. Part e) It is noted in the article that 79 of the subjects were female. Suppose the researchers wish to investigate whether there is a difference in Facebook activity by gender. Based on the data presented here and what you have concluded so far, what approach could you adopt to explore the relationship with gender? O A. Calculate the correlation between word count and gender. B. Pair each of the 20 males with a female subject at random, and then perform a paired t-test involving the differences in the word counts within each pair. C. Include a dummy variable for gender in the linear model fitted. O D. Perform a Chi-squared test for association with gender, with word count as the response variable. O E. Perform a two-sample t-test with the male word count data in one sample, the female word counts in the other