Answer:
Step-by-step 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.
