#30 It is believed that there is a strong relationship between gestational

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Question

#30  For the following five questions refer to this given.

It is believed that there is a strong relationship between gestational age and birth weight. A previous study conducted on 90 infants revealed a correlation coefficient (r) between gestational age and birth weight of 0.6.

Determine whether the population correlation is positive (greater than zero) at the 10% level of significance.

1) The value of t-calculated is: *

a) tcal ~ 7.5

b) tcal ~ -7.36

c) tcal~ -7.5

d) tcal ~ 7.036

2) The decision rule is: *

a) If tcal< tcri then reject H0

b) If tcal> tcri, then reject H1

c) If tcal > tcri, then reject H0

d) None of the above

3) The value of t-critical is *

a) tcrit ~ 1.662

b) tcrit ~ 1.7

c) tcrit ~ 1.291

d) tcrit ~ 1,520

4) The null and the alternate hypotheses are: *

a) H0: ρ > 0 ; H1: ρ = 0

b) H0: ρ < 0 ; H1: ρ ≥ 0

c) H0: ρ ≤ 0 ; H1: ρ > 0

d) H0: ρ < 0 ; H1: ρ > 0

5) The decision in this case is : *

a) H0 is rejected and H1 is accepted

b) H0 is accepted and H1 is rejected

c) H0 and H1 are accepted

d) H0 and H1 are rejected

Answer

Given that a study on n = 90 infants of their age and weight the correlation coefficient is r = 0.60, thus based on the claim the hypotheses are:

1) Test statistic:

Test statistic is caluclated as;

d) tcal ~ 7.036

2) Decision rule :

Since it is a right tailed test, reject Ho if

c) If tcal > tcri, then reject Ho.

3) Critical value:

The critical value for rejection region is computed using the excel formula for t-distribution which is =T.INV(1-0.1, 89)

,WHERE 89 is the degree of freedom and 0.10 is the level of significance .

Thus the tc is computed as 1.291

c) tcrit ~ 1.291

4) based on the claim the hypotheses are:

c) H0: ρ ≤ 0 ; H1: ρ > 0

5) The decision in this case is :

Since the t-calculated is greater than t-critical hence we can reject the null hypothesis and conclude that there is enough evidence to support the claim.

Thus:

a) H0 is rejected and H1 is accepted