1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
guapka [62]
3 years ago
12

A company employs two shifts of workers. Each shift produces a type of gasket where the thickness is the critical dimension. The

average thickness and the standard deviation of thickness for shift 1, based on a random sample of 40 gaskets, are 10.85 mm and 0.16 mm, respectively. The similar figures for shift 2, based on a random sample of 30 gaskets, are 10.90 mm and 0.19 mm. Let µ1-µ2 be the difference in thickness between shifts 1 and 2, and assume that the population variances are equal.
(a) Find a 95% confidence interval for µ1-µ2.
(b) Based on your answer to part a, are you convinced that the gaskets from
shift 2 are, on average, wider than those from shift 1? Why or why not?
(c) How would your answers to parts a and b change if the sample sizes
were instead 300 and 250?
Mathematics
1 answer:
Oksanka [162]3 years ago
6 0

Answer:

a) [-0.134,0.034]

b) We are uncertain

c) It will change significantly

Step-by-step explanation:

a) Since the variances are unknown, we use the t-test with 95% confidence interval, that is the significance level = 1-0.05 = 0.025.

Since we assume that the variances are equal, we use the pooled variance given as

s_p^2 = \frac{ (n_1 -1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2},

where n_1 = 40, n_2 = 30, s_1 = 0.16, s_2 = 0.19.

The mean difference \mu_1 - \mu_2 = 10.85 - 10.90 = -0.05.

The confidence interval is

(\mu_1 - \mu_2) \pm t_{n_1+n_2-2,\alpha/2} \sqrt{\frac{s_p^2}{n_1} + \frac{s_p^2}{n_2}} = (-0.05) \pm t_{68,0.025} \sqrt{\frac{0.03}{40} + \frac{0.03}{30}}

= -0.05\pm 1.995 \times 0.042 = -0.05 \pm 0.084 = [-0.134,0.034]

b) With 95% confidence, we can say that it is possible that the gaskets from shift 2 are, on average, wider than the gaskets from shift 1, because the mean difference extends to the negative interval or that the gaskets from shift 1 are wider, because the confidence interval extends to the positive interval.

c) Increasing the sample sizes results in a smaller margin of error, which gives us a narrower confidence interval, thus giving us a good idea of what the true mean difference is.

You might be interested in
B
klio [65]
Sqrt of 125
10^2 +b^2= 15^2
100 +b^2=225
B^2=125
No perfect square for 125 so leave it in radical form
3 0
3 years ago
Melanie uses the ordered pairs (2010, 48) and (2013, 59) to find her equation. Tracy defines x as the number of years since 2010
rewona [7]
They will have same slopes but different Y intercepts.
5 0
3 years ago
Read 2 more answers
What number is a common factor of 16 and 56
igomit [66]

Answer:

8

Step-by-step explanation:

8 x 2 = 16

8 x 7 = 56

Can I get brainliest

8 0
2 years ago
Read 2 more answers
1, 6, 36, 216 what comes next
scZoUnD [109]

Answer:

The answer is 1296

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Please use answer and step by step explanation
kotykmax [81]
I believe its C. because you have to solve for x.
5 0
3 years ago
Read 2 more answers
Other questions:
  • Carly wants to add texting to her cell phone plan. She has two choices in texting packages. The TURKEY plan charges $.15 per tex
    6·1 answer
  • A square rotated about its center by 360º maps onto itself at different angles of rotation. You can reflect a square onto itself
    15·2 answers
  • Which monomial is a perfect cube? <br> 16x6<br> 27x8 <br> 32x12 <br> 64x6
    15·2 answers
  • The perimeter of triangle RXA is 24. If RX = 4 and RA = 11, find XP and PA
    15·1 answer
  • (2, 7) and (-4,1)<br> In point slope form
    5·1 answer
  • HELP PLEASE! if a||b what is the value of x?
    14·1 answer
  • Which of the following statements are true ?????
    13·1 answer
  • Choose any number, add 3. and then multiply by 6.
    14·2 answers
  • Pls, help due in 30 mins!! it is math.
    12·2 answers
  • PLS help me Order four and seven tenths repeating, negative four and eight ninths, 490%, and −4.9 from least to greatest.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!