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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?

Respuesta :

Answer:

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

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 26.70 inches

Sample mean, [tex]\bar{x}[/tex] = 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

[tex]H_{0}: \mu = 26.70\text{ inches}\\H_A: \mu \neq 26.70\text{ inches}[/tex]

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

Formula:

[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]z_{stat} = \displaystyle\frac{26.77 - 26.70}{\frac{0.20}{\sqrt{48}} } = 2.425[/tex]

Now, [tex]z_{critical} \text{ at 0.05 level of significance } = 1.96[/tex]

Since,

[tex]z_{stat} > z_{critical}[/tex]

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.

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