4. The students of a Statistics class want to estimate how many years it takes for a university professor to earn a PhD. They survey 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)

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

Answer Link

jainveenamrata jainveenamrata · Answer 2 · 2022-03-08T08:27:21+01:00

The interval is from 5.4 - 1.96 (1.6/√40) to 5.4 + 1.96 (1.6/√40). Then the correct option is C.

What is a statistic?

Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, summarise the data.

The students of a Statistics class want to estimate how many years it takes for a university professor to earn a Ph.D.

They survey 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.

The 95% confidence interval is given.

[tex]\rm \mu = 5.4\\\\ \sigma = 1.6\\\\x = 40[/tex]

We know that the formula

[tex]\rm \mu \ \pm \ z \ \dfrac{\sigma}{\sqrt{x}}[/tex]

The value of z for a 95% confidence interval is 1.960.

For the positive signs, we have

[tex]5.4 + 1.96 \dfrac{1.6}{\sqrt{40}}[/tex]

For the negative sign, we have

[tex]5.4 - 1.96 \dfrac{1.6}{\sqrt{40}}[/tex]

Then the interval will be

[tex]5.4 \pm 1.96 \dfrac{1.6}{\sqrt{40}}[/tex]

More about the statistic link is given below.

https://brainly.com/question/10951564