Question

In: Statistics and Probability

Statistical concept for engineering manager: manufacturer’s claim that the strength of the steel connectors they produce...

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.

Solutions

Expert Solution

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.


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