Question

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 14 countries where this information is available for the year 2011 are in following table (note: outlier data has been removed):

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.  

(i) Which of the following statements correctly define both the null hypothesis H_O and the alternate hypothesis 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 are correct

(ii) Enter the level of significance ? used for this test, and the degrees of freedom df:

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 coefficient r between 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

Recommended online calculator:

Correlation and Linear Regression Calculator Applet

(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

Recommended online calculator:

Correlation Coefficient - Testing Significance

(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

Recommended online calculator:

Correlation Coefficient - Testing Significance

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

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 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

Answer 1

i) Null And Alternative Hypothesis : Answer. Option D) None of the above

ii) Level of significance, degrees of freedom

Significance level = 0.05

Degrres of freedom =  (n-2) = (14-2)=12

Answer: 0.05, 12

iii ) The Correlation coefficient is

r = 0.0675

iv) Under H0, the test statistic is

Answer: t = +0.23

v) The P-Value is 0.819

vi) Since p value is greater than significance level. Fail to Reject H0

vii) Answer: 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.