In: Statistics and Probability
19. An aircraft manufacturer requires bolts that are part of the landing gear assembly to have a mean diameter of 1.1 inches with a variance of no more than 0.04 inches2. The bolts are purchased from an outside supplier. A random sample of 30 bolts from a recently received shipment yielded a variance of 0.054 inches2. Should the shipment be returned? Perform the appropriate test of hypothesis using alpha = 0.05. (15 points) T
est Statistic = ______________
Reject Region: Reject H0 x^2 if > ______________
Conclusion: ______________
Conclusion about shipment: ______________
Solution :
The null and alternative hypotheses are as follows :
inches
inches
To test the hypothesis we shall use chi-square test of variance. The test statistic is given as follows :
Where, is sample variance, n is sample size and is hypothesized value of population variance under H0.
We have, n = 30,
The value of the test statistic is 39.15.
Significance level (α) = 0.05
Degrees of freedom = (n - 1) = (30 - 1) = 29
Since, our test is right-tailed test, therefore we shall obtain right-tailed critical value of chi-square at 0.05 significance level and 29 Degrees of freedom which is given as follows:
Rejection Region : Reject H0 if χ2 > 42.557
Conclusion : Since, value of the test statistic is less than the right-tailed critical value of chi-square i.e. the value of the test statistic is not falling in the critical region, therefore we shall be fail to reject the null hypothesis (H0) at 0.05 significance level.
Conclusion about shipment : Since, we have rejected the null hypothesis, therefore we don't have sufficient evidence to conclude that the variance of bolts of recently received shipment is more than 0.04. Hence, the shipment should not be returned.
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