1) A medical researcher wanted to compare two different methods (A and B) for measuring cardiac output (L/min). Method A is the "gold standard" but is invasive (involves inserting a catheter into the main heart artery). Method B is less accurate but is non-invasive. To control for differences between persons, both methods are used on each person participating in the study. This allows measurements to be directly compared for each method, per individual. Cardiac output for 19 subjects was measured by both methods and some summary statistics of the data are summarized in the table below. Is there enough evidence to conclude that the cardiac output for method B is less than the cardiac output for method A on average at a significance level of 0.1.

Cardiac Method	n	Average	Standard deviation
A	19	5.63	1.72
B	19	5.18	1.89
Difference (d = A - B)	19	0.45	0.71

Perform a statistical test. (a) What are the null and alternative hypotheses? H₀: H_A: (b) What is the test statistic? (Round your answer to 3 decimal places, if needed.) (c) Using the statistical table, the p-value is________ ( 0.01 < p-value < 0.025 0.025 < p-value < 0.05 0.05 < p-value < 0.10 p-value > 0.10 0 < p-value < 0.005 0.005 < p-value < 0.01 .) (d) Based on the p-value___________ (reject or fail to reject) the null hypothesis. (e) This data________ (provides or does not provide) sufficient evidence to conclude that the cardiac output for method B is, on average_____ (less than or more than) the same amount as the cardiac output for method A.

2) Having done poorly on a particular exam in a junior high school, 24 students decide to write the exam again to try and improve their mark. Results are given in the following table.

Student	n	Average	Standard deviation
Attempt 1 (A1)	24	51	3.8
Attempt 2 (A2)	24	54	4.1
Difference (d = A1 - A2)	24	-3.0	3.1

(a) Find an 80% confidence interval for the difference in mean scores between attempt 1 and attempt 2. (Round your answers to 4 decimal places, if needed.) (b) Based on this confidence interval, can we conclude there is a difference in mean scores between attempt 1 and attempt 2?

a) No, since the interval is completely below 0.

b) Yes, since the interval contains 0.

c) Yes, since the interval is completely below 0.

d) No, since the interval contains 0.

3) Many college and university students obtain summer jobs. A professor wanted to determine whether students in different degree programs earn different amounts. She randomly selected five students in each of the 4 university programs and asked them to report what they earned the previous summer (in thousands of dollars). The following partially filled-in ANOVA table was obtained. Fill-in the rest of the table. (Use exact values for df and round all other numbers to 2 decimal places, if needed.)

Source	df	SS	MS	F-Stat
Treatments		12.1
Error
Total		24.2