Question

A chemical process has produced, on the average, 800 tons of chemicals per day. The daily yields for the past week are 785, 805, 790, 793, and 802 tons. The sample standard deviation is s = 8.34.

(a) Do these data indicate that the average yield is less than 800 tons? Formulate and test an appropriate hypothesis using α=0.05.

(b) Find the bounds on the p-value for this test.

Answer 1

Solution

The sample mean is

Mean = (x / n) )

=785+805+790+793+8025

=39755

=795

= 800

=795

S = 8.34

n = 5

a ) This is the left  tailed test .

The null and alternative hypothesis is ,

H0 :    = 800

Ha : < 800

Test statistic = t

= ( - ) / S / n

= (795-800 ) / 8.34 / 5

= -1.340

Test statistic = t = -1.340

b ) P-value =0.1256

= 0.05  

P-value >

0.1256 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that