1 ) Ten randomly selected people took an IQ test A, and next day they took a very similar IQ test B. Their scores are shown in the table below.

Person	A	B	C	D	E	F	G	H	I	J
Test A	116	103	104	112	88	74	99	85	94	119
Test B	116	105	109	117	86	74	103	87	96	122

 

 

1. Consider (Test A - Test B). Use a0.05significance level to test the claim that people do better on the second test than they do on the first. (Note: You may wish to use software.)

(b) The test statistic is ______

(c) The critical value is ______

2. Construct a 95% confidence interval for the mean of the differences. Again, use (Test A - Test B). 
 ____<μ< ____

3) 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 n1−1 and n2−1 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:

        Sample Size    Estimated Average Number

                                   (SD) of Words Spoken per Day

Study	Women	Men	Women	Men
1	65	65	15433 (7554)	16692 (9157)
2	30	21	16258 (7503)	12060 (8130)

 

Readers are expected to understand this to mean, for example, the 65 women in the first study hadx¯ = 15433 and s = 7554.

It is commonly thought that women talk more than men. Does either of the two samples support this idea? For each study:

(a) What degrees of freedom does Option 2 use to get a conservative P-value?

Study 1:  
Study 2: 

(b) Compare your value of t with the critical values in Table C. What can you say about the P- value of the test? 
Study 1: P- value >  ____
Study 2:  __≤ P- value ≤ __

4) Test the given claim using the α=0.01 significance level and assuming that the populations are normally distributed. 
Claim: The treatment population and the placebo population have the same mean. 
Treatment group: n=6, x¯=136, s=6.3. 
Placebo group: n=11, x¯=146, s=6.1.

(a) The negative critical value is_____ .

(b)The positive critical value is _____ .