Question

QUESTION 6 Using top secret University records, Dr. Rasmussen determines that 68.2% of MEEN students have IQs between 120 and 150, with an average of 135. Dr. Rasmussen also tests 4 randomly selected MEEN 260 students and finds the average IQ is 140 with a sample deviation of 20" We are 90% certain that the average MEEN 260 student has an IQ greater than: O A 140 (to.05, 3)(10) В 140+(20,45)(10) O C. 140(to.10, 3)(10) D 140 (z0.45)(15) 135(z0.45) (15) O F. 140 (to.o5, 3)(20) O G135 (zo.475)(10) H 140(to.05, 3)(10) O1. 135 (zo.45)(10) o J. 135 (z0.4 5) (20) O K 135 - (to.10, 3)(20) OL 140 (to.os, 3)(15) M. 135 (z0.475)(15 NThe correct answer is not listed 0 O. 140-(t0.10, 3)(10) o P. 135 (zo.45)(15)

Answer 1

we are interested in a lower tailed confidence interval

As the sample size is too small.

Assumption Sample is approximately normal and randomly selected So, we will use t- distribution

$\overline{x}-t_{0.10,3} \frac{s}{\sqrt{n}}$

$140-t_{0.10,3} \frac{20}{\sqrt{4}}=140-(t_{0.10,3})10$

$(o)\ 140-(t_{0.10,3})(10)$