4. Your investment advisor proposes a monthly income investment scheme which promises a variable income each month. You will invest in it only if you are assured an average monthly income of at least 550 dollars. Your advisor also tells you that, for the past 61 months, the scheme had incomes with an average value of 583 dollars and a standard deviation of 111 dollars. (a) Createa 99% confidence interval for the average monthly income of this scheme. (Round your answers to 4 decimal places, if needed.) ( ____,____)

12. It is believed that animals living in northern regions have shorter appendages than animals living in southern regions. Random samples of birds were selected from each group and wing lengths for birds (in millimeters) were measured. The following table gives summary statistics.

Region	n	Average	Standard deviation
Northern (N)	33	110.5	1.7
Southern (S)	33	112.2	3.5
Difference (d = N - S)	33	-1.7	1.6

(a) Find a 95% confidence interval for the mean difference of wing lengths of birds between the northern regions and the southern regions. (Round your answers to 4 decimal places, if needed.) ( ____,____)

13. A clinic compared healthy dogs it owned with healthy pets brought to clinic to be neutered. The summary statistics for blood cholesterol levels (milligrams deciliter of blood) appear in the following table:

Types	n	Average	Standard deviation
Pets (P)	51	197	69.3
Clinic (C)	51	173	44.9
Difference (d = P - C)	51	24.0	51.1

(a) Find a 99% confidence interval for the difference in mean blood cholesterol levels dogs brought to the clinic (P) and dogs owned by the clinic (C). (Round your answers to 4 decimal places, if needed.) ( ____,____) (b) Based on this confidence interval, can we conclude there is some differences in mean blood cholesterol levels between the two groups?

• No, since the interval is completely above 0.
• Yes, since the interval contains 0.
• Yes, since the interval is completely above 0.
• No, since the interval contains 0.