Question

How do I solve this? Preferably in Excel

Clip is produced for safety product that is 6cm. If clip does not meet standards, it is rejected and returned. Getting a high number of clips back and manufacturer wants to check if process is working correctly. Random sample of 100 parts with mean with of 6.25 and st.dev. Of .10. Conduct a hypothesis test at the .01 level of significance.

a. State null and alternative hypothesis b. Calculate the test statistic

c. Find the critical value d. Find the p-value

e. State the decision based on the p-value and critical value f. State the conclusion

Answer 1

Solution
Given in the Question
Null Hypothesis H0: Mean = 6cm
Alternate Hypothesis H1: Mean is not equals 6cm
Also no. of samples = 100
Mean = 6.25 and SD = 0.10
Here we will use t test
Test statistic can be calculated as
test statistic = (Xbar - mean)/SD/sqrt(n) = (6.25-6)/0.10/sqrt(100) = 0.25/0.10/10 = 2.5/0.10 = 25
crircal value for this is at Degree of freedom = (100-1)=99 and this is a two tailed test and alpha=0.01
so tcritical from t table is +/-2.6264
p-value can be calculated from t table also so p-value is = 0.00001
from the p-value we can see that our p-value is less than alpha value so we will reject the null hypothesis against alternate hypothesis.
from the tcritical value we can see that test statistic value is more than test crical value(25>2.6264) so we will reject the null hypothesis.
The conclusion is process is not working correctly.