Question

Having done poorly on their Math final exams in​ June, six students repeat the course in summer school and take another exam in August. If these students are representative of all students who might attend this summer school in other​ years, do these results provide evidence that the program is​ worthwhile? Use a = 0.05. Assume all conditions and assumptions have been satisfied.

Student   June    August
A   52   49
B   52   68
C   68   74
D   70   66
E   65   73
F   64   75

Calculate the test statistic.

t = _ ? (Round to three decimal places as​ needed.)

Calculate the​ P-value

P-value = _ ? (Rounding to four decimal places.)

Answer 1

: Mean difference between the scores in june and scores in the august (June - August)

If the program is worthwhile; August scores > June scores i.e < 0

Null hypothesis : Ho : = 0

Alternate hypothesis : H1: < 0

Left tailed test;

Sample size : Number students repeted the test = 6

d: difference in the scores (June score - August score)

Sample mean difference

Sample standard deviation of the difference : sd

Student	June	August	d	(d-)	(d-)2
A	52	49	3	8.6667	75.1111
B	52	68	-16	-10.3333	106.7778
C	68	74	-6	-0.3333	0.1111
D	70	66	4	9.6667	93.4444
E	65	73	-8	-2.3333	5.4444
F	64	75	-11	-5.3333	28.4444
			=-34		(d-)2=309.3333
			= -5.6667

Test Statistic = -1.765

For left tailed test :

Degrees of freedom = n-1 =6-1 =5

For 5 degrees of freedom, P(t<-1.7647)=0.0689

P-value = 0.0689

As P-Value i.e. is greater than Level of significance i.e (P-value:0.0689 > 0.05:Level of significance); Fail to Reject Null Hypothesis

There is not sufficient evidence to conclude that < 0

i.e

There is not sufficient evidence to conclude that the program is worthwhile