Statistical Analysis of Diameter of a Product

STATISTICS
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1) The relevant hypotheses are as defined below.
H0: μ = 0.75 inch
H1: μ ≠ 0.75 inch
Considering that the population standard deviation is not known, hence t statistics would be
used. This given test would be one sample two tail test.
Sample mean diameter = 0.8125 inch
Sample standard deviation = 0.15625 inch
Sample size = 35
Standard error = (0.15625/√35) = 0.026411
T statistic = (0.8125-0.75)/0.026411 = 2.366
Taking, the significance level as 5%, degree of freedom = 35-1 = 34, the critical t values are
+2.03 and -2.03.
It is evident that the computed t statistic value (2.366) does not lie in the interval defined by -
2.03 and +2.03. As a result, the null hypothesis would be rejected and alternative hypothesis
accepted (Flick, 2015). Hence, it can be concluded that the diameter of the product is
different from the intended 0.75 inch.
2) The relevant hypotheses are as defined below.
H0: μ = 0.75 inch
H1: μ ≠ 0.75 inch
Considering that the population standard deviation is not known, hence t statistics would be
used. This given test would be one sample two tail test.
Sample mean diameter = 0.8125 inch
Sample standard deviation = 0.15625 inch
Sample size = 35