Homework 6-1
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School
University of California, San Diego *
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Course
180A
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
Pages
2
Uploaded by DrThunder12841
HOMEWORK
6
PSTAT 5A – Fall 2023
1. Unit 6 Self-Assessment Quiz (Optional)
2. The amount of time it takes for water to boil at sea level is normally distributed with a mean time of
7.5 minutes and a variance of 1.5625 minutes
2
. Calculate the minimum sample size needed to ensure
that, with 95% confidence, the population mean amount of time it takes to boil water at sea level is
within 0.36 minutes of the estimated mean.
3. Keqiao, China is world renowned for textile manufacturing and production.
A prospective client is
interested in the mean time it takes workers at a particular factory to manufacture their new premium
stuffed plushy. They select a random sample of 30 manufacturing times and calculate the mean length
of time to be 17.56 minutes, with a standard deviation of 1.2 minutes. Assume the manufacturing time
is normally distributed.
(a) Define the parameter of interest.
(b) Define the random variable of interest.
(c) Name the distribution used to construct the confidence intervals. (Check any relevant criteria.)
(d) Construct a 98% confidence interval for the population mean manufacturing time of the premium
plushy.
(e) Interpret your confidence interval for the population mean time to manufacture a premium plushy.
4. Charlie is interested in the mean weight of a newborn beagle puppy from Daisy Hill Puppy Farm.
He selects 8 beagle puppies at random and calculates the mean weight to be 8.2 ounces. Assume the
weight of a newborn beagle puppy from Daisy Hill Puppy Farm is known to be normally distributed
with a standard deviation of 2.5 ounces.
(a) Define the parameter of interest.
(b) Define the random variable of interest.
(c) Name the distribution used to construct the confidence intervals. (Check any relevant criteria.)
(d) Construct a 99% confidence interval for the population mean weight of newborn beagle puppies
from Daisy Hill Puppy Farm.
(e) Interpret your confidence interval for the population mean time to manufacture a premium plushy.
5. The length of time to complete a PSTAT 5A homework is normally distributed with a standard
deviation of 1.6 hours. A graduate student in the UCSB Gevirtz School of Education claims that the
mean time to complete the homework is greater than 4.1 hours. They (with the help of your PSTAT 5A
professor) randomly select 25 students and record how long they spend on their homework assignments.
They calculate the mean time to completion to be 4.2312 hours. Test the graduate students claim at
the 5% significance level.
(a) Define the parameter and random variable of interest.
(b) State the null and alternative hypotheses, and identify the claim.
(c) Determine the distribution of the test statistic. (Check relevant criteria.)
(d) Calculate the test statistic.
(e) Find the p-value.
(f) State your decision.
(g) State your conclusion.
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