The World Bank collected data on the percentage of GDP that acountry spends on health expenditures ("Health expenditure," 2013)and also the percentage of women receiving prenatal care ("Pregnantwoman receiving," 2013). The data for the countries where thisinformation is available for the year 2011 are in followingtable:

Data of Health Expenditure versus PrenatalCare

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 spenton health expenditure and the percentage of women receivingprenatal care. Then compute a 95% prediction interval for thepercentage of woman receiving prenatal care for a country thatspends 5.0 % of GDP on health expenditure.

(i) Which of the following statements correctly defineboth the null hypothesis H_Oand the alternatehypothesis H_A ?

A.   H_O:  ? = 0   H_A:  ? < 0

B.     H_O:  ? > 0   H_A:  ? = 0

C.   H_O:  ? = 0   H_A:  ? > 0

D.     none of these answers arecorrect

(ii) Enter the level of significance ? used forthis test, and the degrees of freedomdf:

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

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

(iii)   Use technology to determinecorrelation coefficient r between independent variable(percent GDP spent on healthcare) and dependent variable (percentwomen 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 andenter test statistic

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

–2.10     –0.07        +0.60       +1.09

(v) Using tables, calculator, or spreadsheet: Determineand 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 and ? value, which isthe correct decision to make for this hypothesistest?  

A. Reject H_o

B. Fail to reject H_o

C. Accept H_o

D. Accept H_A

Enter letter corresponding to correct answer.

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

A. The result is statistically significant at .05 levelof significance. Evidence supports the claim that there is acorrelation between percent GDP spent on healthcare and percentageof women receiving prenatal care.

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

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

D. The result is not statistically significant at .05level of significance.   There is not enough evidence toshow that there is a correlation between percent GDP spent onhealthcare and percentage of women receiving prenatalcare.

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 thepercentage of woman receiving prenatal care for a country thatspends 5.0 % of GDP on health expenditure. Do this by:

• finding t_c(two-tailedt-score using level of significance and df valuefound 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 regressionequation y^ =mx_o + b

• determining bound E using the followingformula: (s_e , n , sample mean for x , andsample variance for x all can be found usinghttp://vassarstats.net/index.html )

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

• subtract, then add bound E to y^ valueto create prediction interval.

Determine which of the following 95% predictionintervals 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 correctanswer

(x) Which of the following statements correctlyinterprets the significance of the predictioninterval?

A. We estimate with 95% confidence that the interval39.42% < y < 116.41% contains the true percentage ofwomen receiving prenatal care for a 5.0% of GDP expenditure onhealthcare.

B. We estimate with 95% confidence that the interval47.65% < y < 108.19% contains the true percentage ofwomen receiving prenatal care for a 5.0% of GDP expenditure onhealthcare.

C. We estimate with 95% confidence that the interval40.89% < y < 114.94% contains the true percentage ofwomen receiving prenatal care for a 5.0% of GDP expenditure onhealthcare.

D. We estimate with 95% confidence that the interval23.29% < y < 132.55% contains the true percentage ofwomen receiving prenatal care for a 5.0% of GDP expenditure onhealthcare.