Question

6.251 Exercise 6.250 describes pulse rates collected from 10 students, once during a quiz and once during a lecture. the data are given in table 6.23 and stored in quiz pulse 10. we might expect mean pulse rates to increase under the stress of a quiz. use the information in exercise 6.250 and the data in table 6.23 to test whether the data provide sufficient evidence to support this claim. conduct a March paired test and explain why a matched paired test is appropriate.

matched pairs not march

Answer 1

We have to test  mean pulse rates to increase under the stress of a quiz.

We have to use matched paired t-test because here we are taking observation on same 10 student for two different situations.In such situationwe shoulduse  matched paired t-test .

Here we have

mean of pulse rate of student in quiz is 68.8

mean of pulse rate of student in lecture is 66.1

sample SD  of pulse rate of student in quiz is 12.5

sample SD  of pulse rate of student in lecture  is 12.8

Thus

Now we have,

											Total	mean	s
Quiz	75	52	52	80	56	90	76	71	70	66	688	68.8	12.506
Lecture	73	53	47	88	55	70	61	75	61	78	661	66.1	12.80148
Difference	2	-1	5	-8	1	20	15	-4	9	-12	27	2.7
(diff -mean diff)2	0.49	13.69	5.29	114.49	2.89	299.29	151.29	44.89	39.69	216.09	888.1

Standard deviation of difference is

We test below hypothesis

H0: mean of pulse rate of student in quiz = mean of pulse rate of student in lecture

Ha: mean of pulse rate of student in quiz >  mean of pulse rate of student in lecture

t= (Mean_Q - Mean_L)/ (Sd/sqrt(n))

=(68.8-66.1)/(9.93/sqrt(10))

=0.859834

P-value

p(T(df=9)> 0.8598)= 0.2614

P-value=0.2614

Critical Value= t(0.025,9)=2.26

t < critical Value We do not reject H0

Conclusion

Hence there is no sufficient evidence to support this claim of mean pulse rates to increase under the stress of a quiz