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Class: Statistics for Linguistics Students Exercises Week3 Assignment due 01-11-2004 Dr Bettina Braun 1) The mean pause duration in a read text is 200ms with a standard deviation of 50ms. For the calculations please specify how you reached your conclusion! a. Is this a statistic or a parameter? b. What proportion of the data is above 70ms? c. What proportion of the data falls between 100ms and 300ms? 2) If we have a sample size of 50, what does the sampling distribution of the means look like if the population is a) U-shaped, b) skewed-left, and c) normally distributed? 3) What happens, if the sample size increases for the following statistics. Does the a. estimated mean increase, decrease, or stay approximately the same? Why? b. standard error increase, decrease, or stay approximately the same? Why? 4) What are the dependent and independent variables in the following research questions? Please state the null hypothesis. a. Does the gender influence the fundamental frequency (pitch) in adults? b. Does the gender have an effect on the fundamental frequency (pitch) in children under 10? c. Imagine you have a text-to-speech synthesis system. You are interested to find out whether the acceptability (from 1 to 5) is increased if you model short pauses at syntactic phrases. d. Is the proportion of consonants to vowels the same in English, Italian, German, and Spanish? e. Subjects learned 20 nonsense-words presented visually. 30 minutes later they were tested for retention. The next day, the same subjects learned another 20 nonsense-words, this time in a combined visual and auditory presentation. Again, after 30 minutes they were tested for retention. The researcher measured the number of correct nonsense-words. f. To study the duration of words in repeated production, twenty subjects read paragraphs in which the same words appeared 4 times. Are words produced shorter if they are repeated? g. A group of university students was given a test and depending on the responses, they were grouped according to extroversion. Then they were asked to write an email to their mother, a friend and to a professor. Does extroversion correspond with the use of linguistic means (e.g. punctuation, sentence length)? 5) What is the type of dependent variable (interval, ordinal, frequency data) for the above experiments? How many levels do the independent variables have in each of the research questions? 6) Please fill the cells of the table with “Type I error”, “Type II error”, and “correct decision” True state of affairs No difference Difference exists Reject H0 Accept H0 7) Download the dataset for week3. a. You’ll find 3 columns of variables, the first being the year of the exam (1990 and 2000), the second the gender (starting with males), the third the score. Please name and label the variables correctly, b. Draw the 95% confidence interval for females and males (for both exam years). Do the distributions look much different? Report the mean and the standard deviation for female and male scores. c. Draw the 95% confidence interval for males and females, grouped according to the exam year. Describe the general tendencies for the four distributions (e.g. were females on average better than males were?) Please submit the assignment in electronic form, naming the file <initials>_statstut1