The following Exercise is based on summary statistics rather than raw data. This
ID: 3238547 • Letter: T
Question
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 conservative Option 2 (degrees of freedom the smaller of n_1 - 1 and n_2 - 1 for two-sample t confidence intervals and P-values. You must trust that the authors understood the conditions for inference and verified 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: Readers are expected to understand this to mean, for example, the 64 women in the first study had x bar = 15551 and s = 7773. 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 terms of the population mean number of words spoken per day for men (mu_M) and for women (mu_F). If necessary, use ! = to represent notequalto. (b) Find the two-sample t statistic to test mu_F - mu_M. (c) What degrees of freedom does Option 2 use to get a conservative P-value?Explanation / Answer
The statistical software output for study 1 and study 2 is:
Two sample T hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 0
(without pooled variances)
Hypothesis test results:
Hypothesis test results:
Hence,
b) Study 1: 0.81
Study 2: -1.7179
c) Study 1: 63
Study 2: 18
Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 1221 1507.3232 122.50229 0.81004524 0.4195