Question

A manufacturer claims that the mass of an electronic component he produces is 2g with a standard deviation of 0.1g. He takes a sample of 50 components and finds that the mean mass is found to be 2.04g. Assuming that the mass is normally distributed, test the hypothesis that the mean mass is 2g at the 2% level of significance.

Answer 1

Solution:

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: The mass of an electronic component produced is 2g.

Alternative hypothesis: Ha: The mass of an electronic component produced is not 2g.

H0: µ = 2 versus Ha: µ ≠ 2

This is a two tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 2

Xbar = 2.04

σ = 0.1

n = 50

α = 0.02

Critical value = -2.3263 and 2.3263

(by using z-table or excel)

Z = (2.04 - 2)/[0.1/sqrt(50)]

Z = 2.8284

P-value = 0.0047

(by using Z-table)

P-value < α = 0.02

So, we reject the null hypothesis

There is not sufficient evidence to conclude that the mass of an electronic component produced is 2g.