A certain type of stainless steel powder is supposed to have

A certain type of stainless steel powder is supposed to have a mean particle diameter of p = 10 pm. A random sample of 100 particles had a mean diameter of 10.116 pm, with a sample standard deviation of 0.5 pm. A test is made of H_0: mu = 10 versus H_1 mu 10. Find the P value for H_0. Do you believe it is plausible that the mean diameter is 10 pm, or are you convinced that it differs from 10 pm? Explain your reasoning.

Solution

We are given that the hypothesis that,

H0 : µ = 10 Vs H1 : µ 10

where µ is population mean.

The test is two sided.

Assume alpha = 0.05

sample size (n) = 100

mean diameter (Xbar) = 10.116

sample standard deviation (sd) = 0.5

Here sample size is large but population standard deviation is unknown and information regarding sample is given so we use t-test.

The test statistic is,

t = (Xbar - µ) / (sd/sqrt(n))

t = (10.116 - 10) / (0.5/sqrt(100) )

t = 2.32

We can finnd P-value by using EXCEL.

syntax :

TDIST(x, d.f., tails)

where x is test statistic value.

d.f. = n - 1 = 100 - 1 = 99

tails = 2

P-value = 2*0.022 = 0.044

Assume alpha = 0.05

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : The population mean is differ from 10 µm.