Question

Two statistics professors at two rival schools decide to use IQ scores as a measure of how smart the students at their respective schools are. IQ scores are known to be Normally distributed. The two professors will use this knowledge to their advantage. They will randomly select 10 students from their respective schools and determine the students' IQ scores by means of the standard IQ test. The two professors will use the pooled version of the two-sample t test to determine whether the students at the two universities are equally smart. Let 47 and 42 represent the mean IQ scores of the students at the two universities. Let on and be the corresponding population standard deviations. The hypotheses they will test are Ho: 41 - U2 = 0 versus Ha: 47 - US 70. Based on the two samples of 10 students, the two professors find that a = 111, # = 120, 51 = 7, and so = 11. Suppose the professors had wished to test the hypotheses Ho: 11 = 12 versus Ha: 1 < 12. Using the graphing calculator, what can we say about the value of the Pvalue? O 0.01 < Pvalue < 0.025 O Pvalue < 0.01 O 0.025< Pvalue < 0.05 o Pvalue > 0.05

Answer 1

Solution-1:

its 2 p values u get

For 2 tail test

Ho:mu1-mu2=0

Ha:mu1-mu2 not =0

using t i83 calculator

TESTS>2-SampTTest

TI-83 Plus TEXAS INSTRUMENTS 2-SampTTest 1.1#uz TEXAS INSTRUMENTS TI-83 Plus 2-SameTTest tn1:10 X2: 120 SX2:11 12:10 w.1:#uz <2 22 Pooled:No Yes Calculate Draw azaz9525 12 TARE F5 STATPLOTF: TEISET 2 FORMAT F3 CALCE Y= WINDOW ZOOM TRACE STATPLOT F GRAPH TSEY F2 FORMAT WINDOW ZOOM CAC TRACE TABLE FS GRAPH QUIT MODE QUITING 2nd A-LOCK INS DEL LIST LINK

we get

p=0.045

No we do one tail test

Ho:mu1=mu2

Ha:mu1<mu2

TI-83 Plus TEXAS INSTRUMENTS 2-SampTTest NICK2 TEXAS INSTRUMENTS TI-83 Plus 2-SameTTest tn1:10 X2: 120 SX2:11 n2:10 1:32 KZ 2 Pooled: No Yes Calculate Draw Ans+ SAINTPLOTF: TELSET P2PORMAT 3 CAC WINDOW ZOOM TRACE TABLE GRAPH BTNTPLOT FETISEY F2 FORMATS CALCE WINDOW ZOOM TRACE TABLE FS GRAPH YE Ya INE QUIT MODE 2nd DEL

p=0.0225

SELECT

0.025<p<0.05

ANSWER:

0.025<p<0.05

Solution-2:

pooled t test we do when we have equal variance

you can assume the two populations have equal variances

MARK OPTION A