Question

Question To test H:160 versus H, H<60, a random sample of size n=24 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. Click here to view the t-Distribution Area in Right Tal. (m) 1 x - 57.1 and 12.6, compute the text statistic. 1-Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a= 0.1 level of significanos, determine the critical value(s). Although technology oral-distribution table can be used to find the critic value, in this problem use the t-distribution table given. Critical Value: (Round to three decimal places. Use a comma to separate answers as needed.)

Answer 1

Given,

n = 24

$Ho: \mu = 60$

$Ha: \mu < 60$

=> Left-sided test.

(a) X = 57.1 and s = 12.6

Standard error SE = s/ = 2.57

'n

t-statistic = ( ) / SE = (57.1-60)/2.57 = -1.128

H-X

(b) $\alpha$ = 0.1

Since n = 24 => df = 23

For these values, the critical value can be calculated from a t-distribution table.

critical value = -1.3194

(c) Since this is a left-sided test, hence critical region will be in left tail. Also, -1.3194 is on somewhere left to the centre.

Hence the correct graph is c.

(d)

Since test-statistic does not fall in the critical region i.e. t > critical value

Hence we cannot reject the null hypothesis.

Correct choice is B