(1.5 points) If the standard deviation of hole diameter exceeds 0.01 millimeters

Question

(1.5 points) If the standard deviation of hole diameter exceeds 0.01 millimeters, there is an unacceptably high probability that the rivet will not fit. Suppose that n = 15 and s = 0.008 millimeters.
a. Is there strong evidence to indicate that the standard deviation of hole diameter exceeds 0.01 millimeters? Use a = 0.01. State your conclusions explicitly. What does rejecting or not rejecting null hypothesis mean?
b. Find the P-value for this test.
c. Suppose that the actual standard deviation of hole diameter exceeds the hypothesized value by 50%. What is the beta in part (a)? Show ?.
d. If s is really as large as 0.0125 millimeters, what sample size will be required to defect this with power of at least 0.8? Show ?.

Explanation / Answer

given that                  n=15,s=0.008 a) Ho=s=0.01 H1=s>0.01    by using chisquare test =(n-1)(s^2)/(s^2)                        = 14(0.008*0.008)/0.0001                          =8.96          the tabulated value of  chi square deg. of freedom at 14 is 6.57                    here   calucated chisquare> tabulted chisquare therefore we reject the null hypothsis          b) the p value is                          p(chisquare<tab of chisquare)         therefore we reject the null hypothsis          b) the p value is                          p(chisquare<tab of chisquare)        

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