Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears measured in foot-pounds is
an important characteristic. A random sample of 10 gears from supplier 1 results in $$\overline{\mbox{x}}_1=290$$ and $$s_1 = 12$$, and another random sample of 16 gears from the second supplier results in $$\overline{\mbox{x}}_2=321$$ and $$s_2 = 22$$.
a. Is there evidence to support the claim that supplier 2 provides gears with higher mean impact strength? Use α = 0.05, and assume that both populations are normally distributed but the variances are not equal.
What is the P-value for this test?
b. Do the data support the claim that the mean impact strength of gears from supplier 2 is at least 25 foot-pounds higher than that of supplier 1? Make the same assumptions as in part (a).
c. Construct a confidence interval estimate for the difference in mean impact strength, and explain how this interval could be used to answer the question posed regarding supplier-to-supplier differences.
a. Is there evidence to support the claim that supplier 2 provides gears with higher mean impact strength? Use α = 0.05, and assume that both populations are normally distributed but the variances are not equal.
What is the P-value for this test?
b. Do the data support the claim that the mean impact strength of gears from supplier 2 is at least 25 foot-pounds higher than that of supplier 1? Make the same assumptions as in part (a).
c. Construct a confidence interval estimate for the difference in mean impact strength, and explain how this interval could be used to answer the question posed regarding supplier-to-supplier differences.
1 answer:
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Answer:
Null hypothesis:
Alternative hypothesis:
Step-by-step explanation:
1) Data given and notation
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
2) State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 8000, the system of hypothesis are :
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
3) Calculate the statistic
We can replace in formula (1) the info given like this:
4) P-value
Since is a one-side upper test the p value would given by:
5) Conclusion
If we compare the p value and the significance level assumed, for example we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean is significantly higher than $8000.