Question 1 An article in Engineering Horizons (Spring 1990, p. 25) reported that

Question

Question 1 An article in Engineering Horizons (Spring 1990, p. 25) reported that 117 of 484 new engineering graduates were planning to continue studying for an advanced degree. Consider this as a random sample of the 1990 graduating class Round your answers to 3 decimal places. (a) Find a 90% confidence interval on the proportion of such graduates planning to continue their education. (b) Find a 95% confidence interval on the proportion of such graduates planning to continue their education. (c) The 90% confidence interval is ce interval.

Explanation / Answer

a)
p = 117/484 = 0.2417 , n = 484
z value at 90% CI = 1.645

CI = p +/- z* sqrt(p *(1-p)/n)
= 0.2417 +/- 1.645 * sqrt( 0.2417 * 0.7583/484)
= 0.2097 , 0.2737
0.2097 < p < 0.2737

b)

p = 117/484 = 0.2417 , n = 484
z value at 95% CI = 1.96
CI = p +/- z* sqrt(p *(1-p)/n)
= 0.2417 +/- 1.96 * sqrt( 0.2417 * 0.7583/484)
= 0.2036 , 0.2798
0.2036 < p < 0.2798

c)The 90% confidence interval is less than 95% confidence interval

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