Question

A certain type of stainless steel powder is supposed to have a mean particle diameter of µ = 15µm. A random sample of 87 particles had a mean diameter of 15.2 µm, with a standard deviation of 1.8 µm. A test is made of H0 :µ = 15 versus H1 :µ =!15. a. Find the P-value. b. Do you believe it is plausible that the mean diameter is 15 µm, or are you convinced that it differs from 15 µm? Explain your reasoning.

Answer 1

We conclude that mean diameter is not equal to 15 µm.

Explanation:

We are given the following in the question:

Population mean, μ = 15

Sample mean,
`\bar{x}` = 15.2

Sample size, n = 87

Alpha, α = 0.05

Sample standard deviation, σ = 1.8

First, we design the null and the alternate hypothesis

`H_(0): \mu = 15\\H_A: \mu \\eq 15`

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

Formula:

`t_(stat) = \displaystyle\frac{\bar{x} - \mu}{(s)/(√(n-1)) }` Putting all the values, we have

`t_(stat) = \displaystyle(15.2-15)/((1.8)/(√(86)) ) = 1.03`

Now,

`t_(critical) \text{ at 0.05 level of significance, 86 degree of freedom } = \pm 1.9879`

Since,

`|t_(stat)| < |t_(critical)|`

We reject the null hypothesis and fail to accept it.

P-value is 0.3

Since p-value < 0.05

We reject the null hypothesis and accept the alternate hypothesis and conclude that mean diameter is not equal to 15 µm.

Both the approaches that the that mean diameter is not equal to 15 µm.