A parent interest group is looking at whether birth order
affects scores on the ACT test. It was suggested that, on average,
first-born children earn lower ACT scores than second-born
children. After surveying a random sample
of 175 first-born children, the parents’ group found that
they had a mean score of 24.3 on the ACT. A survey
of 100 second-born children resulted in a mean ACT score
of 24.8. Assume that the population standard deviation for
first-born children is known to be 2.2 points and the
population standard deviation for second-born children is known to
be 1.9 points. Is there sufficient evidence at
the 1% level of significance to say that the mean ACT
score of first-born children is lower than the mean ACT score of
second-born children? Let first-born children be Population 1
and let second-born children be Population 2.
Step 1 of 3:
State the null and alternative hypotheses for the test. Fill in
the blank below.
H0: μ1=μ2:
Ha: μ1⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯μ2
Step 2 of 3:
Compute the value of the test statistic. Round your answer to
two decimal places.
Step 3 of 3:
Draw a conclusion and interpret the decision.