STAT 200 week 7

Problem 1:

The table below contains the value of the house and the amount of rental income in a year that the house brings in when rented. Answer all parts (a) through (e).

(a) Create a scatter plot of the data. What kind of association does the scatter plot suggest (e.g., positive linear, etc.)

(b) Using technology (e.g., Excel's Regression Tool or the TI 84 calculator), determine the following:

(i) Find the linear correlation coefficient "r". Provide an interpretation.

(ii) Find the coefficient of determination "R²". Provide an interpretation.

(iii) Find the equation of the least squares regression line between the value of the house and the amount of rental income in a year that the house brings in when rented.

(c) Using the equation from part (b)(iii), find the following:

(i) Estimate the rental income for a house worth $230,000;

(ii) Estimate the rental income for a house worth $400,000.

(d) Which rental income that you calculated in part(c) is a more accurate estimate of the true rental income? Why?

(e) Test at the 5% level for a positive correlation between house value and rental amount. Specifically, do the following:

(i) Set up the appropriate null and alternative hypotheses.

(ii) Verify that the assumptions necessary to apply the test are satisfied.

(iii) What is the test statistic and what is the p-value?

(iv) State your conclusion.

Table: Data of House Value versus Rental

Value	Rental	Value	Rental	Value	Rental	Value	Rental
81000	6656	77000	4576	75000	7280	67500	6864
95000	7904	94000	8736	90000	6240	85000	7072
121000	12064	115000	7904	110000	7072	104000	7904
135000	8320	130000	9776	126000	6240	125000	7904
145000	8320	140000	9568	140000	9152	135000	7488
165000	13312	165000	8528	155000	7488	148000	8320
178000	11856	174000	10400	170000	9568	170000	12688
200000	12272	200000	10608	194000	11232	190000	8320
214000	8528	208000	10400	200000	10400	200000	8320
240000	10192	240000	12064	240000	11648	225000	12480
289000	11648	270000	12896	262000	10192	244500	11232
325000	12480	310000	12480	303000	12272	300000	12480

Problem 2:The World Bank collected data on the percentage of GDP that a country spends on health expenditures and also the percentage of women receiving prenatal care. The data for the countries where this information are available for the year 2011 is in the table below. Answer all parts (a) through (e).

(a) Create a scatter plot of the data. What kind of association does the scatter plot suggest (e.g., positive linear, etc.)

(b) Using technology (e.g., Excel's Regression Tool or the TI 84 calculator), determine the following:

(i) Find the linear correlation coefficient "r". Provide an interpretation.

(ii) Find the coefficient of determination "R²". Provide an interpretation.

(iii) Find the equation of the least squares regression line between percentage spent on health expenditures and the percentage of women receiving prenatal care.

(c) Using the equation from part (b)(iii), find the following:

(i) Estimate the percent of women receiving prenatal care for a country that spends 5.0% of GDP on health expenditures;

(ii) Estimate the percent of women receiving prenatal care for a country that spends 12.0% of GDP on health expenditures.

(d) Which prenatal care percentage that you calculated in part (c) do you think is closer to the true percentage? Why?

(e) Test at the 5% level for a correlation between percentage spent on health expenditures and the percentage of women receiving prenatal care. Specifically, do the following:

(i) Set up the appropriate null and alternative hypotheses.

(ii) Verify that the assumptions necessary to apply the test are satisfied.

(iii) What is the test statistic and what is the p-value?

(iv) State your conclusion.

Table: Data of Health Expenditure versus Prenatal Care

Health Expenditure (% of GDP)	Prenatal Care (%)
9.6	47.9
3.7	54.6
5.2	93.7
5.2	84.7
10.0	100.0
4.7	42.5
4.8	96.4
6.0	77.1
5.4	58.3
4.8	95.4
4.1	78.0
6.0	93.3
9.5	93.3
6.8	93.7
6.1	89.8

Problem 3:

Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities (travel, feed, social) the dolphins partake in at certain times of the day. The numbers in the table below represent the number of groups of dolphins that were partaking in an activity at certain times of days.

Set up and run a test of hypothesis to determine ifthere is enough evidence to show that the activity and the time period are independent for dolphins. Use a level of significance of 1%. Specifically, do the following:

(i) Write down the null and alternative hypotheses.

(ii)Verify that the assumptions necessary to apply the test are satisfied.

(iii) What is the test statistic and what is the p-value?

(iv) State your conclusion

Table: Dolphin Activity

Activity	Period	Row Total
Morning	Noon	Afternoon	Evening
Travel	6	6	14	13	39
Feed	28	4	0	56	88
Social	38	5	9	10	62
Column Total	72	15	23	79	189

Problem 4.

A person's educational attainment and age group were collected by the U.S. Census Bureau in 1984 to see if age group and educational attainment are related. The counts in thousands are in the table below.

Set up and run a test of hypothesis to determine ifthere is enough evidence to show that educational attainment and age are independent. Use a level of significance of 5%. Specifically, do the following:

(i) Write down the null and alternative hypotheses.

(ii)Verify that the assumptions necessary to apply the test are satisfied.

(iii) What is the test statistic and what is the p-value?

(iv) State your conclusion

Table: Educational Attainment and Age Group

Education	Age Group	Row Total
25-34	35-44	45-54	55-64	>64
Did not complete HS	5416	5030	5777	7606	13746	37575
Competed HS	16431	1855	9435	8795	7558	44074
College 1-3 years	8555	5576	3124	2524	2503	22282
College 4 or more years	9771	7596	3904	3109	2483	26863
Column Total	40173	20057	22240	22034	26290	130794

Problem 5.

In Africa in 2011, the number of deaths of a female from cardiovascular disease for different age groups are in the table below. Also, the proportion of deaths of females from all causes for the same age groups are in the table.

Set up and run a test of hypothesis to determine ifdeaths from cardiovascular disease are in the same proportion as all deaths for the different age groups. Use a level of significance of 5%. Specifically, do the following:

(i) Write down the null and alternative hypotheses.

(ii)Verify that the assumptions necessary to apply the test are satisfied.

(iii) What is the test statistic and what is the p-value?

(iv) State your conclusion

Table: Deaths of Females for Different Age Groups

Age	Cardiovascular Frequency	All Cause Proportion
"5 - 14"	8	0.10
"15 - 29"	16	0.12
"30 - 49"	56	0.26
"50 - 69"	433	0.52
TOTAL	513

Problem 6.

A project conducted by the Federal Office of Road Safety asked people many questions about their cars. One question asked was: "What is the primary reason that a person chooses a particular car?" The data is contained in the table below.

Table: Reason for Choosing a Car

SAFETY	84
RELIABILITY	62
COST	46
PERFORMANCE	34
COMFORT	47
LOOKS	27
TOTAL	300

Set up and run a test of hypothesis to determine ifthe frequencies observed substantiate the claim that the reasons for choosing a car are equally likely. Use a level of significance of 5%. Specifically, do the following:

(i) Write down the null and alternative hypotheses.

(ii)Verify that the assumptions necessary to apply the test are satisfied.

(iii) What is the test statistic and what is the p-value?

(iv) State your conclusion