Question 8
Researchers investigating characteristics of gifted children
collected data from schools in a large city on a random sample of
thirty-six children who were identified as gifted children soon after
they reached the age of four. The following histogram shows the
distribution of the ages (in months) at which these children first
counted to 10 successfully. Also provided are some sample statistics.
Suppose
you read online that children first count to 10 successfully when they
are 32 months old, on average. You perform a hypothesis test evaluating
whether the average age at which gifted children first count to 10 is
different than the general average of 32 months. What is the p-value of
the hypothesis test? Choose the closest answer.
"N=36"
"\\overline{x}=30.69"
"\\sigma=4.31"
"H_0" : The mean age is 32 months to count to 10; "\\mu=32"
"H_a" : The mean age is less than 32 months to count to 10; "\\mu<32"
Test Statistic:
"z=\\frac{\\overline{x}-\\mu}{\\sigma\/\\sqrt{N}}=\\frac{30.69-32}{4.31\/\\sqrt{36}}=-1.82"
p-value:
"p=P(z<-1.82)=0.034"
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