In IQ test was given to a simple random sample of 70 students at a certain college. The sample mean score was 106.4. Scores on this test are known to have a standard deviation of σ=10. It is desired to construct a 90% confidence interval for the mean IQ score of students at this college.

(a) What is the point estimate?

Answer:

A) The point estimate $(x\bar)=106.4$

B) The confidence interval:

→ The significance level $(\alpha) = 1 – 0.90 = 0.10$

→ The critical value $(z_c )= Z_{\frac{\alpha}{2}} = Z_{\frac{0.10}{2}} = 1.64$
→ Now, The 90% confidence interval :

$$CI = \overline{x} \pm z_c \cdot \frac{\sigma}{\sqrt{n}} = 106.4 \pm 1.64 \cdot \frac{10}{\sqrt{70}} = (104.432, 108.368)$$