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 660 dollars. Your advisor also tells you that, for the past 41 months, the scheme had incomes with an average value of 708 dollars and a standard deviation of 92 dollars. (a) Createa 99% confidence interval for the average monthly income of this scheme. (Round your answers to 4 decimal places, if needed.) ( ______,______ ) (b) Based on this confidence interval, should you invest in this scheme?

Yes, since the interval contains 660.

No, since the interval contains 660.

Yes, since the interval is completely above 660.

No, since the interval is completely above 660.

9. Do skiers spend less than golfers on their vacations? To help answer this question, a travel agency surveyed 41 customers who regularly take their partners on a skiing vacation and 41 customers who regularly take their partners on a golf vacation. The amounts spent on vacations last year are shown in the following table. Perform an appropriate hypothesis test and use a significance level of 0.1.

	n	Average	Standard deviation
Skiers (S)	41	2749	308
Golfers (G)	41	3448	630
Difference (d = S - G)	41	-699	555

(a) What are the null and alternative hypotheses? H₀:

p / / pS - pG / S - G / d

< / / > / =

0 / -699

H_A:

p / / pS - pG / S - G / d

= / / / < / / >

0 / -699

(b) What is the test statistic? (Round your answer to 3 decimal places, if needed.) (c) Using the statistical table, the p-value is 0.005 < p-value < 0.01 / 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 . (d) Based on the p-value, the travel agency should reject / fail to reject the null hypothesis. (e) This data provides / does not provide sufficient evidence to conclude that the skiers spend, on average, less than / more than / the same amount as golfers on their vacations.

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)	30	113.9	1.8
Southern (S)	30	115.2	3.7
Difference (d = N - S)	30	-1.3	1.6

(a) Find an 80% 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.) ( ______,______ ) (b) Based on this confidence interval, is there enough evidence to support the belief?

No, since the interval is completely below 0.

No, since the interval contains 0.

Yes, since the interval contains 0.

Yes, since the interval is completely below 0.

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	190	68.3
Clinic (C)	51	179	40.3
Difference (d = P - C)	51	11.0	45.2

(a) Find a 95% 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?

Yes, since the interval is completely above 0.

Yes, since the interval contains 0.

No, since the interval is completely above 0.

No, since the interval contains 0.