Question

A standardized test for high school students is given to a random sample of 16 students. The average time required to finish the test for the students in the sample is recorded as 48 minutes with a standard deviation of 6 minutes. We want to evaluate the null hypothesis that the time required to finish the test for the whole population of high school students is at most 45 minutes on average.

Assuming , which one below describes the rejection region?

		The region to the right of 1.753
		The region to the left of -1.753
		The region to the left of -2.131
		The region that lies to the left of -1.753 plus the region that lies to the right of 1.753
		The region to the right of 2.131
		The region that lies to the left of -2.131 plus the region that lies to the right of 2.131

level of significance 0.05

Answer 1

Solution :

Given that ,

= 45  

= 48

s = 6

n = 16

The null and alternative hypothesis is ,

H0 :   = 45

Ha :     45

This is the left tailed test .

Test statistic = T

= ( - ) / s / n

= ( 48 - 45 ) / 6 / 16

= 2

The test statistic = 2

= 0.05  

df = n - 1 = 16 - 1 = 15

t ,df = t0.05 ,15 = -1.753

t < -1.753

The critical value = -1.753

Answer = The region to the of -1.753

.