Question

You are working on a manufacturing process that should produce products that have a diameter of 3/4 of an inch. You take a random sample of 35 products and find the diameter to be 13/16 of an inch with a standard deviation of 5/32 of an inch. Considering a 5% level of significance, what can you state statistically about the process? Please include a null hypothesis, an alternative hypothesis, and use an appropriate test statistic (i.e. ZSTAT or tSTAT).

Answer 1

Answer)

Null hypothesis Ho : u = 3/4

Alternate hypothesis Ha : u not equal to 3/4

As the population s.d is unknown here we will use t distribution to conduct the test

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = ((13/16)-(3/4))/((5/32)/√35)

t = 2.37

Degrees of freedom is = n-1 = 34

For 34 dof and 2.37 test statistics

P-value from t distribution is = 0.0236

As the obtained p-value is less than 0.05 (given significance level)

We reject the null hypothesis Ho

So we do not have enough evidence to support the claim.that u = 3/4