Question

The soup produced by a company has a salt level that is normally distributed with a mean of 5.4 grams and a standard deviation of 0.3 grams. The company takes readings of every 10th bar off the production line. The reading points are 5.8, 5.9, 4.9, 5.2, 5.0, 4.9, 6.2, 5.1, 5.7, 6.1. Is the process in control or out of control and why?

Answer 1

Explanation:

The mean of the reading points is

Mean = (5.8 + 5.9 + 4.9 + 5.2 + 5.0 + 4.9 + 6.2 + 5.1 + 5.7 + 6.1)/10 = 5.48

The process is out of control if the mean salt level of the readings is greater than 5.4

For the null hypothesis,

µ = 5.4

For the alternative hypothesis,

µ > 5.4

This is a right tailed test.

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 5.4

x = 5.48

σ = 0.3

n = 10

z = (5.48 - 5.4)/(0.3/√10) = 0.84

Looking at the normal distribution table, the probability corresponding to the z score is 0.7996

The probability value to the right of the z score is 1 - 0.7996 = 0.2

Assuming a significance level of 0.05

Since alpha, 0.05 < than the p value, 0.2, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, we can conclude that the process is not out of control. If we had rejected the null hypothesis, then our conclusion would be that the process is out of control.