Question

Calibrating a scale:

Answer 1

Answer:

We conclude that the calibration point is set too high.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ =  1000 grams

Sample mean, $\bar{x}$ =  1001.1 grams

Sample size, n = 50

Alpha, α = 0.05

Population standard deviation, σ = 2.8 grams

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 1000\text{ grams}\\H_A: \mu > 1000\text{ grams}$

We use One-tailed(right) z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{ 1001.1 - 1000}{\frac{2.8}{\sqrt{50}} } = 2.778$

Now, $z_{critical} \text{ at 0.01 level of significance } = 2.326$

Since,  

$z_{stat} > z_{critical}$

We reject the null hypothesis and accept the alternate hypothesis. We accept the alternate hypothesis. We conclude that the calibration point is set too high.