In: Statistics and Probability
Statistical concept for engineering manager:
manufacturer’s claim that the strength of the steel connectors they produce is 400 Mpa. To verify the correctness of this, engineers collected 4 samples. The strength measurements were; 440, 449, 425 and 432 Mpa. Do the data indicate that the true mean exceeds 400 Mpa. Test the hypothesis using α = 0.01.
Here, we have to use one sample t test for the population mean.
The null and alternative hypotheses are given as below:
Null hypothesis: H0: the true mean is 400 Mpa.
Alternative hypothesis: Ha: the true mean exceeds 400 Mpa.
H0: µ = 400 versus Ha: µ > 400
This is an upper tailed test.
The test statistic formula is given as below:
t = (Xbar - µ)/[S/sqrt(n)]
From given data, we have
µ = 400
Xbar = 436.5
S = 10.34408043
n = 4
df = n – 1 = 3
α = 0.01
Critical value = 4.5407
(by using t-table or excel)
t = (Xbar - µ)/[S/sqrt(n)]
t = (436.5 - 400)/[ 10.34408043/sqrt(4)]
t = 7.0572
P-value = 0.0029
(by using t-table)
P-value < α = 0.01
So, we reject the null hypothesis
There is sufficient evidence to conclude that the true mean exceeds 400 Mpa.