Misconceptions about everyday scientific phenomena, such as die seasons, gravity
ID: 2918395 • Letter: M
Question
Misconceptions about everyday scientific phenomena, such as die seasons, gravity and light, are common in the general population. To assess die degree to which university students about to receive a middle school teaching credential shared these misconceptions, a science quiz consisting of 10 multiple-choice questions was given to a random sample of 52 such students. Let X denote the number of correct responses (out of 10). For this sample, the sample mean was 5.14 and we'll use an estimated sigma = 1.30. Give a 90% confidence interval for the mean quiz score. Suppose the sample size was increased to 165 students (assume same x ) Suppose the sigma estimate was revised to .98, recalculate the 90% confidence interval. Comment on the effects of sample size and standard deviation on the confidence intervals.Explanation / Answer
Given n=52, xbar=5.14, =1.3 (a)=0.1, Z(0.05)=1.645 (check normal table) The 90% CI is xbar± Z*/n -->5.14 ± 1.645*1.3/sqrt(52) -->( 4.843, 5.437) (b) n=165 The 90% CI is xbar± Z*/n -->5.14 ± 1.645*1.3/sqrt(165) -->( 4.974, 5.306) (c)=0.98 The 90% CI is xbar± Z*/n -->5.14 ± 1.645*0.98/sqrt(52) -->( 4.916, 5.364)