![katemsoo](/avatars/35443.jpg)
katemsoo
11.04.2020 •
Mathematics
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 x1=290 and s1=12, and another random sample of 16 gears from the second supplier results in ¯x2=321 and s2=22. Assume that both populations are normally distributed and the variances are equal. Use α=0.05.
(a) Is there evidence to support the claim that supplier 2 provides gears with higher mean impact strength?
(b) Calculate the P-value for the above test in part (a) and make a conclusion on the test.
(c) construct a 95% confidence interval estimate for the difference in mean impact strength between supplier 2 and supplier 1.
(d) Explain how the interval constructed in part (c) could be used to test the claim that the mean impact strength of gears from supplier 2 is at least 25 foot-pounds higher than that of supplier 1.
Solved
Show answers
More tips
- F Food and Cooking How to Determine Healthy, Nutritious Food for Yourself?...
- S Style and Beauty How to Get Rid of a Bruise: Tips and Tricks...
- F Food and Cooking Лечо: вкусное и простое блюдо для любой кухни...
- H Health and Medicine Relieving Swelling in Legs: Causes and Ways to Alleviate the Symptom...
Answers on questions: Mathematics
- M Mathematics Simplify the expression...
- M Mathematics The graph of an exponential function is given. Which of the following is the correct equation of the function? 9 3- 2 1 1 2 3 x 文 -4 -3 -2 -1 -1 -2+ -3 a. y = 0.45...
- M Mathematics A company has 4,500 customers and wants to gain 15% more customers each quarter. The executives want to project when the company will reach certain milestones to...
- M Mathematics Question 8 (3 points) Determine the x and y intercepts for the line 3x – 5y + 15 = 0. Show your work....
- M Mathematics the following data represent the number of people aged 25-64 years covered by health insurance (private or government) in 2018. approximate the mean and standard deviation...
- M Mathematics Write an equation for a line that is perpendicular to the line 6y – 9x = 12...
- M Mathematics In some country the budget for defense exceeded the budget for education by $629.1 billion. If x represents the budget for education, in billions of dollars, how can...
- M Mathematics I’m not sure why it won’t let me input this answer? Is it wrong? What’s the right answer?...
- M Mathematics 3y=150, what is the value of y-2...
- M Mathematics Please help??? An explanation would help too and the answers...
Ответ:
(a) There is enough evidence to support the claim that supplier 2 provides gears with higher mean impact strength.
(b) p-value = 0.033.
(c) The 95% confidence interval estimate for the difference in mean impact strength between supplier 2 and supplier 1 is (-64.26, 2.26).
(d) The null hypothesis is rejected.
Step-by-step explanation:
Let X₁ denotes plastic gear manufactured by supplier 1 and X₂ denotes plastic gear manufactured by supplier 2.
The given information is,
(a)
The hypothesis for the test can be defined as:
H₀: There is no difference between the mean impact strength of the gears provided by the two suppliers, i.e. μ₁ - μ₂ = 0.
Hₐ: The means impact strength of the gears provided by the supplier 2 is higher, i.e. μ₁ - μ₂ < 0.
It is assumed that the two populations are normally distributed and the variances are equal.
We will use a t-test to perform the test.
The t-statistic is given by,
Compute the pooled standard deviation as follows:
Compute the test statistic as follows:
The, t-statistic value is -1.92.
The degrees of freedom of the test is:
df = (n₁ + n₂ - 2) = 24
Decision rule:
If the test statistic value is less than the critical value then the null hypothesis will rejected.
The critical value is:
*Use a t-table.
The test statistic value is less than the critical value.
Thus, the null hypothesis will be rejected at 5% level of significance.
So, there is enough evidence to support the claim that supplier 2 provides gears with higher mean impact strength.
(b)
For the computed t-statistic and (n₁ + n₂ - 2) degrees of freedom, the p-value will be,
Use the t-table.
The p-value of the test is less than the significance level . Thus, the null hypothesis is rejected.
Concluding that there is enough evidence to support the claim that supplier 2 provides gears with higher mean impact strength.
(c)
The 95% confidence interval is:
Thus, the 95% confidence interval estimate for the difference in mean impact strength between supplier 2 and supplier 1 is (-64.26, 2.26).
(d)
A confidence interval can be used to test the claim made.
If the confidence interval consist the null value of the parameter then the null hypothesis will be accepted or else rejected.
The alternate hypothesis to be tested is:
Hₐ: The mean impact strength of gears from supplier 2 is at least 25 foot-pounds higher than that of supplier 1, i.e. μ₁ - μ₂ ≥ - 25
The 95% confidence interval estimate for the difference in mean impact strength consist the difference values less than 25 foot-pounds.
Thus, the null hypothesis is rejected.
Ответ:
The answer will be 1.95 y. Hope this helps! Please give brianliest. :)
Step-by-step explanation: