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(2 points) The following Exercise is based on summary statistics rather than raw data. This information is typically all that is presented in published reports. You can calculate inference procedures by hand from the summaries. Use the consenrative Option 2 (degrees of freedom the smaller of n1 1 and n1 1 for two-sample t condence intenrais and P-values. You must trust that the authors understood the conditions for inference and veried that they apply. This isn't always true.) Equip male and female students with a small device that secretly records sound for a random 30 seconds during each 12.5-minute period over two days. Count the words each subject speaks during each recording period, and from this, estimate how many words per day each subject speaks. The published report includes a table summarizing six such studies. Here are two of the six: Sample Size Estimated Average Number (SD) of Words Spoken per Day Study Women Men Women Men 1 56 56 15268 (1744) 16657 (9275) 2 26 21 16383 0902) 12012 (8285) Readers are expected to understand this to mean, for example, the 58 women in the first study had E = 15268 and s = 7744. It is commonly thought that women talk more than men. Does either of the two samples support this idea? For each study: (a) State the alternative hypothesis in tems of the population mean number of words spoken per day for men 01M) and for women (up). If necessary, use != to represent #. Study 1: I'M I'F Study 2: MM [4F (b) Find the two-sample t statistic to test up In". Study 1: Study 2: (c) What degrees of freedom does Option 2 use to get a conservative P-value? Study 1: Study 2: (d) Compare your value oft with the critical values in Table 0. What can you say about the P- value ofthe test? Study 1: P- value > Study 2: 5 P- value 5