Question

Extensive data collected during the first half of this century showed clearly that in those years,...

Extensive data collected during the first half of this century showed clearly that in those years, American-born Japanese childern grew faster than did Japanese-born children. A research paper conjectured that improved economic and environmental conditions in postwar Japan had greatly narrowed this gap. To investigate the validity of this conjecture, a large sample of Hawaiian-born Japanese children was obtained, and the children were categorized with respect to age. There were 15 11-year-old boys in the sample. The sample average height of these 15 boys was 136.24 cm and the sample standard deviation was 6.63 cm. The average height of native-born-11-year-old Japanese children at that time was known to be 131.91 cm. Does this data suggest that the true average height of Hawaiian born male exceeds their native-born counterpart? Use t test. (α = 0.05) H0: μ= 131.91 versus H1: μ> 131.91 Let μdenote the true average height for all Hawaiian-born 11-year-old male Japanese children.

Reject Null Hypothesis

Fail to Reject Null Hypothesis

Homework Answers

Answer #1

H0:Null Hypothesis: = 131.91

HA: Alternative Hypothesis: >131.91

SE = s/

= 6.63/ = 1.7119

Test statistic is:

t = (136.24 - 131.91)/1.7119 = 2.5294

= 0.05

ndf = n - 1 = 15 - 1 = 14

One Tail - Right Side Test

From Table, critical value of t = 1.7613

Since the calculated value of t = 1.7613 is less than critical value of t =2.5294, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that the true average height of Hawaiian born male exceeds their native - born counterpart.

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