Q$5.$ Wenzhou is a toy supplier company in China manufacturing wooden construction sets of

various styles. In the production process, the number of pieces of the wooden construction sets is

required to be $70$ pieces including nuts, bolts, drilled bars to connect and a child$-$size screwdriver.

If the number of pieces is more than $70$ the drilled bars in the sets are pared back to the required

number of pieces. However, if the number of pieces is significantly less than $70,$ they can not be

used and are sent to another production area where they are re$-$size to use in the assembly of

standard unit blocks. In the production of the unit blocks it is known that the standard deviation of

the process is $2\mathrm{.}5$ and the quality control audit of the company takes a random sample with the

number of pieces for each set according to the following table:

a$.$ Formulate the appropriate hypothesis testing structure and compute test statistic to test

whether the average number of pieces for wooden construction sets is less than $70$ at $5\%$

significance level?

b$.$ Calculate p$-$value for the hypothesis test in Part a and explain whether your answer

corroborate with the conclusion obtained.

c$.$ Assume that the process standard deviation is not known. Conduct "One Sample t$-$Test"

on SPSS at $5\%$ level to test the same hypothesis and interpret your analysis findings.

Explain how it differs from the case that process standard deviation is known. For "Hypothesis Testing" problem, the related tables must be added to your solution file and

SPSS Output File must also be uploaded with.