Question

# Age and Vocabulary Researchers claim that there is significant positive linear correlation between population age and...

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.

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

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