4. The students of a Statistics class want to estimate how many years it takes for a university professor to earn a PhD. They su
rvey a random sample of 40 professors with PhDs, which results in a sample mean of 5.4 years and a standard deviation of 1.6 years. Which of the following represents the 95% confidence interval for the true mean of the number of years it takes a professor to earn a PhD?
(A) 5.4±1.96(1.6)
B) 5.4 ± 1.96 (1.6/40)
C) 5.4±1.96(1.6/√40)
D) 5.4 ± 2.03 (1.6/40)
D) 5.4 ± 2.03 (1.6/√40)
(A) 5.4±1.96(1.6)
B) 5.4 ± 1.96 (1.6/40)
C) 5.4±1.96(1.6/√40)
D) 5.4 ± 2.03 (1.6/40)
D) 5.4 ± 2.03 (1.6/√40)
1 answer:
Answer:
E)
(or second D)
Explanation:
The picture shows the confidence interval and from there you just basically solve each of the answer's equations till you get one that is the same or the closest to the true interval. For this problem the answer was E).
5.4+2.03(1.6/√40)=5.91355
And
5.4-2.03(1.6/√40)=4.88644
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Yaya says:
IQ Scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. What percentage of IQ scores are between 70 and 130?
IQ Scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. What percentage of IQ scores are between 70 and 130?
<span>Solution: </span>130 – 100 = 30 which is 2(15). Thus, 130 is 2 standard deviations to the right of the mean. 100 – 70 = 30 which is 2(15). Thus, 70 is 2 standard deviations to the left of the mean. Since 70 to 130 is within 2 standard deviations of the mean, we know that <span>about 95% of the IQ scores would be between 70 and 130.</span>