Question

There may be an association between a country's birthrate and the life expectancy of its inhabitants. A report this past year, coming from a random sample of 21 countries, contained the following statistic: =r?0.59 for the two variables number of births per one thousand people and female life expectancy. Based on this information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population correlation coefficient ? . (Assume that the two variables have a bivariate normal distribution.) Use the 0.10 level of significance, and perform a two-tailed test. Then fill in the table below. (If necessary, consult a list of formulas.)

The null hypothesis: H0:

The alternative hypothesis: H1:

The type of test statistic:

The value of the test statistic: (Round to at least three decimal places.)

The two critical values at the 0.10 level of significance: (Round to at least three decimal places.) and

Based on the report, can we conclude (using the 0.10 level) that there is a significant linear relationship between number of births per one thousand people and female life expectancy?YesNo ???x

Answer 1

Null Hypothesis , there is no linear relationship between number of births and female life expectancy

Alternative Hypothesis , there is a linear relationship between number of births and female life expectancy

Under H0, the test statisic is

Significance Level

Degrees of freedom = n-1= 21- 2 = 19

The critical value of t for 19 df at 10% signficance level is -1.729 , 1.729

Since calculated value of t does not comes within the range of critical values. Reject H0.

Hence, there is linear relationship between between number of births per one thousand people and female life expectancy.