Question

A manufacturer makes steel rods that are supposed to have a mean length of 50 cm. A retailer suspects that the bars are running short. A sample of 40 bars is taken and their mean length is determined to be 49.4 cm with a standard deviation of 3.6 cm. Test the retailer’s claim that the mean length is less than 50 cm. Use a one percent level of significance.

1. What test should be used for this problem?

2. What is the P-value?

3.

What's the conclusion?

	A.	Fail to reject H0. There is not enough evidence to support the claim that the mean length is less than 50 cm.
	B.	Fail to reject H1. There is enough evidence to support the claim that the mean length is less than 50 cm.
	C.	Reject H0. There is enough evidence to support the claim that the mean length is less than 50 cm.
	D.	Reject H1. There is not enough evidence to support the claim that the mean length is more than 50 cm.

Answer 1

Solution :

t test should be used for this problem

This is the left tailed test .

The null and alternative hypothesis is

H₀ : = 50

H_a : < 50

Test statistic = t

= ( - ) / s / n

= (49.4 - 50) / 3.6 / 40

Test statistic = -1.054

df = 39

P-value = 0.1492

= 0.01

P-value >

Fail to reject the null hypothesis .

Option A) is correct .