Question

The competitive advantage of small American factories such as Tolerance Contract Manufacturing lies in their ability to produce parts with highly narrow requirements, or tolerances, that are typical in the aerospace industry. Consider a product with specifications that cal for a maximum variance in the lengths of the parts of 0.0008. Suppose the sample variance for 30 parts turns out to be
s2 = 0.0009.
Use
α = 0.05
to test whether the population variance specification is being violated.
State the null and alternative hypotheses.
H0: σ2 ≤ 0.000
Ha: σ2 > 0.0008
H0: σ2 = 0.0008
Ha: σ2 ≠ 0.0008
H0: σ2 ≥ 0.0008
Ha: σ2 < 0.0008
H0: σ2 > 0.0008
Ha: σ2 ≤ 0.0008
H0: σ2 < 0.0008
Ha: σ2 ≥ 0.0008
Find the value of the test statistic.
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
A. Reject H0. The sample does support the conclusion that the population variance specification is being violated.
B. Reject H0. The sample does not support the conclusion that the population variance specification is being violated.
C. Do not reject H0. The sample does support the conclusion that the population variance specification is being violated.
D. Do not reject H0. The sample does not support the conclusion that the population variance specification is being violated.

Answer 1

Answer:

1. H0: σ2 ≤ 0.0008

Ha: σ2 > 0.0008

2. test statistic = 32.625

3. p value = 0.2931

4. D

Step-by-step explanation:

s² = 0.0009

alpha = 0.05

σ² = 0.0008 this is the value that we would be testing

1. hypothesis:

H0: σ2 ≤ 0.0008

Ha: σ2 > 0.0008

2. test statistic:

X² = (n-1/σ²)s²

= ((30-1)/0.0008)0.0009

= 32.625

3. p-value:

P(X² > 32.63) = 0.2931

4. conclusion:

the p-value at 0.2931 is greater than alpha at 0.005, (0.2931>0.05). So the correct option is D. we do not reject H0. the sample does not support conclusion that the population variance specification is being violated.