Question

The average IQ of adult population is 100 and are normally distributed. A researcher believes the IQ of adults is lower. A random sample of 7 adults are tested and scored: 69 , 79 , 89 , 99 , 109, 98, 81 Use a significance level of 0.05.

Answer 1

∑x = 624

∑x² = 56770

n = 7

Mean , x̅ = Ʃx/n = 624/7 = 89.1429

Standard deviation, s = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(56770-(624)²/7)/(7-1)] = 13.8134

Null and Alternative hypothesis:

Ho : µ = 100 ; H1 : µ < 100

Test statistic:

t = (x̅- µ)/(s/√n) = (89.1429 - 100)/(13.8134/√7) = -2.0795

df = n-1 = 6

p-value = T.DIST(-2.0795, 6, 1) = 0.0414

Decision:

p-value < α, Reject the null hypothesis

Conclusion:

There is enough evidence to conclude that population mean is less than 100 at 0.05 significance level.