please help, statistics problem?

Question

numerous studies shown that IQ scores have been increasing, generation by generation, for years. The increase is called Flynn Effect, and the data indicate that the increase appears to be about 7 points per decade. To demonstrate this phenomenon, a researcher obtained 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 N=16 of today's highschool students and obtains a sample mean IQ of M=121, with a squared standard deviation of 6000.

Is this result sufficient to conclude that today's sample scored significantly higher than would be expected from a population with a mean 100? use a one-tailed test, with alpha level of .01

thank u, but what does t_0.99 mean?

Answer 1

H0: µ = 100
Ha : µ > 100

Assuming neither the population mean nor population variance is known, the critical region is given by

xbar > 100 + [sqrt(6000)/sqrt(16)] t_0.99

where t _0.99 = 2.602 is the value of the t-distribution with 15 degrees of freedom for α=0.99.

[sqrt(6000)/sqrt(16)] t_0.99 ≈ 50.4 so the critical region is

xbar > 150.4

so we do not reject the null hypothesis.

The 121 figure sure sounds significant, but the variance is quite large and the sample size is small.