HU Stat Questions

STAT 344Homework 6
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Instructions:
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Deadline: December 2nd , 2022, at 11.59PM through Blackboard as a single PDF.
Handwritten solutions must be scanned and submitted as a PDF file.
Typed solutions are acceptable and must be submitted as a PDF file.
Do not submit hard copies in Class.
Do not submit pictures/Photos as multiple files.
Submissions that do not meet all the following criteria will not be graded:
Your solutions will grade for accuracy; all steps must be shown. The solutions are expected to be
of collegiate quality.
Each solution should be:
• Written one question per page
• written darkly.
• Should be easy to follow.
• Must show your work
Be sure that your name in the upper right-hand corner of each page.
See below options for generating a PDF for this exam, Name the file
STAT344HW6_Lastname_Firstname.
Once the PDF has been generated, please view the file to assure its legibility prior to uploading.
You will only be able to upload the file once.
Generating a PDF: Here are some options for generating a PDF:
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CamScanner – PDF Scanner App; free on Android and iOS. You can upload to Google
Drive and Dropbox directly.
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Using “Notes” app on iOS/Apple Devices:
You should practice generating a PDF at least three times prior to the submitting one. Be sure that
the file can be easily viewed on a tablet, iPad, and computer.
I strongly suggest that you create a folder on the device that you will use to store the PDFs for this
course.
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Answer all questions.
1. During the independent research 30 women were chosen to measure their weight. The
mean value of weight is 66 𝑘𝑔 and it is known from the previous experience that the weight
is normally distributed with. 𝜎 = 10 𝑘𝑔
a. Find a 95% confidence interval on the mean weight.
b. Find a 90% confidence interval on the mean weight.
c. Which interval is wider?
2. Following are two confidence interval estimates of the mean µ of the cycles to failure of
an automotive door latch mechanism (the test was conducted at an elevated stress level to
accelerate the failure).
3062.9 £ µ £ 3153.7,
3048.5 £ µ £ 3168.1
a. What is the value of the sample mean cycles to failure?
b. One of these intervals is a 95% CI and the other is a 99% CI. Which one is the
95% CI?
3. During an independent research, 2500 randomly selected people were interviewed
whether they visit their dentist for a regular dental checkup or not. Only 2000 gave a
positive answer.
Calculate a 95% confidence interval on the proportion of people who regularly have a
dental checkup.
4. A research engineer for a tire manufacturer is investigating tire life for a new rubber
compound and has built 16 tires and tested them to end-of-life in a road test. The sample
mean and standard deviation are 60489.7 and 3645.94 kilometers.
The engineer would like to demonstrate that the mean life of this new tire is in excess of
60,000 kilometers. Formulate the appropriate hypotheses. Test the appropriate hypotheses
using𝛼 = 0.05. Is it possible to reject 𝐻! hypothesis at the 0.05 level of significance?
(Assume data is normally distributed).