Question

Numerous studies have shown that IQ scores have been increasing, generation by generation, for years (Flynn, 1984, 1999). The increase is called the Flynn Effect, and the data indicate that the increase appears to be about 7 points per decade. To demonstrate this phenomenon, a researcher obtains an IQ test that was written in 1980. At the time the test was prepared, it was standardized to produce a population mean of 100. The researcher administers the test to a random sample of 16 of today's high school students and obtains a sample mean IQ of 110 with standard deviation of 20. Is this result sufficient to conclude that today's sample scored significantly higher than would be expected from a population with 100? Test this claim at the 5% significance level.

Fill in the blanks with the appropriate responses:

Hypotheses
H₀: The mean IQ score is 100
H₁: The mean IQ score is Blank 1 100
(type in “less than”, “greater than”, or “not equal to”)

Results
t = Blank 2 (enter the test statistic, use 2 decimal places)
p-value = Blank 3 (round answer to nearest thousandth of a percent – i.e. 0.012%)

Conclusion
We Blank 4 sufficient evidence to support the claim that the mean IQ is Blank 5 100 (p Blank 6 0.05).
(Use “have” or “lack” for the first blank, “less than”, “greater than” or “not equal to” for the second blank and “<” or “>” for the final blank)

Answer 1

The appropriate hypotheses are -

H₀: The mean IQ score is 100
H₁: The mean IQ score is greater than 100

Let denotes today's average score.

Conclusion : We have sufficient evidence to support the claim that the mean IQ is not equal to 100.