Question

Age and Vocabulary Researchers claim that there is significant positive linear correlation between population age and vocabulary based on a sample of nine children with correlation coefficient r = 0.841. Test this claim at the 95% confidence level. Select one for each blank.

(a) Hypotheses:

H0: [r, rho, x, mu] [=, >=, <=, >, >] 0

Ha: [r, rho, x, mu] [=, >=, <=, >, <] 0

(b) Type of test: [Two sided, Right sided, Left sided]      

(c) Choice of distribution: [normal, t-distribution, chi-squared distribution]      

(d) Critical value: [1.645, 1.860, 1.895, 1.96, 2.306, 2.365]      

(e) Test statistic value: [0, 0.05, 0.841, 0.95, 1] .Standardized test statistic value: [0.841, 1.96, 2.435, 4.113, 6.289]

(f) Reject or fail to reject: Since the standardized test value is [equal to, greater than, less than] the critical value, we [reject, fail to reject, prove, support] the null.

(g) Interpret: There is enough evidence at the 5% significance level to [support, reject] the claim that there is a significant positive linear correlation between age and vocabulary.  

Answer 1

r=0.841

n=9

95% confidence level

a)

H0: rho= 0

Ha: rho>0

b)

Type of test: right sided one tail test

c)

t-distribution

d)df=n−2=9−2=7

alpha=0.05

right tail

Critical value:2.365

e)

.Standardized test statistic value-

f)

Reject null hypothesis

Since the standardized test value is greater than the critical value, we reject the null.

g)

Interpret: There is enough evidence at the 5% significance level to support the claim that there is a significant positive linear correlation between age and vocabulary