We must take care that we are accurately interpreting the results of our confide

Question

We must take care that we are accurately interpreting the results of our confidence intervals and hypothesis tests. Consider the scenarios described below. We want to find the average height of adult men in America. We choose a SRS of 36 adult American men and perform a 95% confidence interval. Using this procedure we find that their average height is 71 in plus/minus 0.52 inches. (1) What was the average height of the men in our sample? (2) What is the margin of error of this confidence interval? (3) State the lower and upper limits of this confidence interval. Comment on one of the student comments about this scenario is the student correct or are they committing an error? (1) Student A says: This means that if we pick an adult American man at random, there is a 95% chance that he is between 70.48 inches tall and 71.52 inches tall. (2) Student B says: This means that 95% of American men's height are between 70.48 inches and 71.52 inches.

Explanation / Answer

lower limit = 70.48 = x - z * (s/sqrt(n)) .....1)

Upper limit = 71.52 = x + z * ( s/sqrt(n)) .....2)

Add equation 1) and 2)

1)

2x = 142
x = 71
Average height of men in sample = 71

2)

Put x = 71 in equation 1)

70.48 = 71 - 1.96 * ( s / sqrt(36))
1.96 * (s/sqrt(36)) = 0.52
s = 1.59

ME = z * ( s/sqrt(n))

= 1.96 * ( 1.59 / sqrt(36))
= 0.5194

3)
lower limit = x - z * (s/sqrt(n))
= 71 - 1.96 * ( 1.59 / sqrt(36))
= 70.48

Upper limit = x + z * ( s/sqrt(n))   
= 71 + 1.96 * ( 1.59 / sqrt(36))
= 71.52

Student B says : This means that 95% of americn men heights are between 70.48 and 71.52 inches

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.