Question

A business receives supplies of copper tubing where the supplier has said that the average length is 26.70 inches so that they will fit into the business’ machines. A random sample of 48 copper tubes finds they have an average length of 26.77 inches. The population standard deviation is assumed to be 0.20 inches. At α=0.05, should the business reject the supplier’s claim?

Answer 1

The business should reject the supplier's claim as mean length is not equal to claimed value of 26.70 inches.

Explanation:

We are given the following in the question:

Population mean, μ = 26.70 inches

Sample mean,
`\bar{x}` = 26.77 inches

Sample size, n = 48

Alpha, α = 0.05

Population standard deviation, σ = 0.20 inches

First, we design the null and the alternate hypothesis

`H_(0): \mu = 26.70\text{ inches}\\H_A: \mu \\eq 26.70\text{ inches}`

We use Two-tailed z test to perform this hypothesis.

Formula:

`z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }`

Putting all the values, we have

`z_(stat) = \displaystyle(26.77 - 26.70)/((0.20)/(√(48)) ) = 2.425`

Now,
`z_(critical) \text{ at 0.05 level of significance } = 1.96`

Since,

`z_(stat) > z_(critical)`

We reject the null hypothesis and accept the alternate hypothesis. Thus, the business should reject the supplier's claim as mean length is not equal to claimed value of 26.70 inches.