Question

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

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.