The World Bank collected data on the percentage of GDP that a country spends on health expenditures ("Health expenditure," 2013) and also the percentage of women receiving prenatal care ("Pregnant woman receiving," 2013). The data for the countries where this information is available for the year 2011 are in following table:

Data of Health Expenditure versus Prenatal Care

Health Expenditure (% of GDP)

Prenatal Care (%)

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

Test at the 5% level for a correlation between percentage spent on health expenditure and the percentage of women receiving prenatal care. Then compute a 95% prediction interval for the percentage of woman receiving prenatal care for a country that spends 5.0 % of GDP on health expenditure.

(i) Which of the following statements correctly define both the null hypothesisH_Oand the alternate hypothesisH_A?

A.H_O:= 0H_A:< 0

B.H_O:> 0H_A:= 0

C.H_O:= 0H_A:> 0

D. none of these answers are correct

(ii) Enter the level of significanceused for this test, and the degrees of freedomdf:

Enter level of significance in decimal form to nearest hundredth, followed by comma, followed by degrees of freedom value to nearest integer. Do not enter spaces.

Examples of correctly entered answers:0.01,4 0.02,11 0.05,13 0.10,46

(iii) Use technology to determine correlation coefficientrbetween independent variable (percent GDP spent on healthcare) and dependent variable (percent women receiving prenatal care)

Enter in decimal form to nearest ten-thousandth with sign. Examples of correctly entered answers:

-0.0001 +0.0020 -0.0500 +0.3000 +0.7115

(iv)Calculate and enter test statistic

Enter value in decimal form rounded to nearest hundredth, with appropriate sign (no spaces). Examples of correctly entered answers:

-2.10 -0.07 +0.60 +1.09

(v) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest thousandth. Examples of correctly entered answers:

0.000 0.001 0.030 0.600 0.814 1.000

(vi) Comparing p-value andvalue, which is the correct decision to make for this hypothesis test?

A. RejectH_o

B. Fail to rejectH_o

C. AcceptH_o

D. AcceptH_A

Enter letter corresponding to correct answer.

(vii) Select the statement that most correctly interprets the result of this test:

A. The result is statistically significant at .05 level of significance. Evidence supports the claim that there is a correlation between percent GDP spent on healthcare and percentage of women receiving prenatal care.

B. The result is statistically significant at .05 level of significance. There is not enough evidence to show that there is a correlation between percent GDP spent on healthcare and percentage of women receiving prenatal care.

C. The result is not statistically significant at .05 level of significance. Evidence supports the claim that there is a correlation between percent GDP spent on healthcare and percentage of women receiving prenatal care.

D. The result is not statistically significant at .05 level of significance. There is not enough evidence to show that there is a correlation between percent GDP spent on healthcare and percentage of women receiving prenatal care.

Enter letter corresponding to most correct answer

(viii) Determine standard error of the estimates_e:

Enter answer to nearest hundredth

(ix) Compute a 95% prediction interval for the percentage of woman receiving prenatal care for a country that spends 5.0 % of GDP on health expenditure. Do this by:

• findingt_c(two-tailedt-score using level of significance anddfvalue found in part (ii))https://www.danielsoper.com/statcalc/calculator.aspx?id=10
• find "y^" output value corresponding tox_o= 5.0 using line-of-best-fit regression equationy^ =mx_o+ b
• determining boundEusing the following formula: (s_e, n, sample mean for x , and sample variance for x all can be found using http://vassarstats.net/index.html )

E=(tc) (se) (1+1n+( xox )2(sx2)(n1) )E=tc se 1+1n+ xo-x 2sx2n-1

• subtract, then add boundEto y^ value to create prediction interval.

Determine which of the following 95% prediction intervals is most correct:

A. 39.42% <y< 116.41%

B. 23.29% <y< 132.55%

C. 47.65% <y< 108.19%

D. 40.89% <y< 114.94%

Enter letter corresponding to most correct answer

(x) Which of the following statements correctly interprets the significance of the prediction interval?

A. We estimate with 95% confidence that the interval 39.42% <y< 116.41% contains the true percentage of women receiving prenatal care for a 5.0% of GDP expenditure on healthcare.

B. We estimate with 95% confidence that the interval 47.65% <y< 108.19% contains the true percentage of women receiving prenatal care for a 5.0% of GDP expenditure on healthcare.

C. We estimate with 95% confidence that the interval 40.89% <y< 114.94% contains the true percentage of women receiving prenatal care for a 5.0% of GDP expenditure on healthcare.

D. We estimate with 95% confidence that the interval 23.29% <y< 132.55% contains the true percentage of women receiving prenatal care for a 5.0% of GDP expenditure on healthcare.