tudying by English majors follows a N(µ2,2)distribution. A random sample of 16 C

Question

tudying by English majors follows a N(µ2,2)distribution. A random sample of 16 Communications majors and 26 English majors found: Communications: n1=16 ¯ x1=5.5 s1=2.0English: n2=26 ¯ x2=7.3 s2=2.4Assume the population standard deviations are equal, i.e. 1=2.

(a) Suppose we wish to test H0µ1=µ2 vs. Haµ1µ2 at the =0.01 signicance level. Approximate the pvalue for this test using the ttable.

(b) (3 pts) Based upon your answer in 8.3(a), is there a signicant dierence in the population mean study times? Why?

(c) Use the tProbability Applet at http://www.stat.uiowa.edu/~mbognar/applets/t.html to precisely determine the pvalue for the test in 8.3(a).

(d) Find a 99% condence interval for µ1µ2.

Explanation / Answer

(a) Here for subject communications :

n1 =16 ; x1 = 5.5 ; s1 = 2.0

for subject english

n2=26 ; x2 = 7.3 ; s1 = 2.4

Here population variance are equal so we will perfrom t - test for two sample test.

Pooled standard deviation =sqrt [(n1 -1)s12 + (n2 -1)s22 ]/ (n1 + n2 -2)

=sqrt [(15 * 22 + 25 * 2.42 )/40] = 2.258

here

t = ( x1 -  x2)/ [sp * sqrt(1/n1 + 1/n2 )]

t = (5.5 - 7.3)/ [2.258 * sqrt(1/16 + 1/26)]

t = -1.8 / 0.7175 = 2.51

so p - value = Pr(t > 2.51; df = 40) = 0.01 to 0.05

(b) No, as the p - value is greater than the significane level 0.01 so we shall not reject the null hypothesis and can claim that both subjects have same marks.

(c) BY using applet we get t - value = 0.01627

(d) 99% confidence interval for µ1µ2  = ( x1 -  x2) +- t0.01, 40 sp sqrt(1/n1 + 1/n2 )

= (5 .5 - 7.3) +- 2.7045 * 2.258 * sqrt (1/16 + 1/26)

= -1.8 +- 1.94

= (-3.74, 0.14)

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