Question

The scores of a certain population on the Wechsler Intelligence Scale for Children (WISC) are thought to be Normally distributed, with mean μ and standard deviation σ = 10. I wish to test whether the mean for this population differs from the national average of 100, so I use the hypotheses H0: μ = 100 and Ha: μ ≠ 100, based on an SRS of size 25 from the population. I calculate a 95% confidence interval for μ and find it to be 100.76 to 106.24. Which of the following is true?

A. I would reject H0 at level .05.
B. I would reject Ha at level .05.
C. The P-value is .05.
D. A mistake has almost ce

Answer 1

The sample mean is given by
\[\bar {x}=\frac{100.76+106.24}{2}=103.5\]
A 2-tail test is needed. The standard deviation of the national population is not known therefore a t test must be used.
The estimated standard deviation of the national population s = 10
\[t=\frac{\bar {x}-\mu}{\frac{s}{\sqrt{n}}}=\frac{3.5}{2}=1.75\]
The degrees of freedom = 25 - 1 = 24
For 24 degrees of freedom the critical value for t at the 5% level is 2.064
Since 1.75 < 2.064 the null hypothesis is accepted at the 5% significance level.