The heights (in inches) of seventh-grade girl students in a school district on L

Question

The heights (in inches) of seventh-grade girl students in a school district on Long Island are known to be normally distributed. The heights of a random sample of 14 seventh-grade girl students in the school district are shown below.

57.8 64.8 61.7 59.8 62.4 68.7 57.2 57.1 63.0 66.2 58.0 62.6 57.0 60.2

a. Conduct a hypothesis test using =0.01 to show that the population mean height of the school district is lower than 63.0. Suppose that a further study establishes that, in fact, the population mean is 61.5. Did the test in part (a) make a correct decision? If not, what type of error did it make? c.

Explanation / Answer

a. H0  : >= 63.0 cm

Ha : < 63.0 cm

Here sample mean x = 61.1786 inch

sample standard deviation s = 3.6826 inch

standard error of sample mean se0= s/ sqrt(n) = 3.6826/ sqrt(14) = 0.9842 inch

t = (x - H)/ se0  = (61.1786 - 63)/ 0.9842 = -1.85062

Here dF = 14 -1 = 13 and alpha = 0.01

tcritical= t13,0.01 = 2.65031

so here l t l < tcritical so we fail to reject the null hypothesis and can conclude that the population mean height of the school district is not lower than 63.0 inch.

(b) p - value = Pr(t > 1.85062, 13) = 0.0435

(c) Here true population mean is 61.5 so we have not made a correct decision as we havn't rejected the null hypothesis. We have committed a type II error.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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