CI for Proportions
Leandro wants to build a one-sample z interval with 98% confidence to estimate the proportion of light bulbs that arrive broken upon shipment to his store. He takes a random sample of 500 bulbs and finds that 25 arrived broken.
What critical value should Leandro use to construct this confidence interval?
z=2.326
What is the critical value t for constructing a 99% confidence interval for a mean with 11 degrees of freedom?
3.106
When do we use z over t for means?
When we know the population sd AND n > 30
A 95% confidence interval for p is (.34, .41). What was the sample proportion and the ME?
p hat = .375
ME = .035
People applying for a driver's license In California usually need to take a multiple choice test as a part of the application process. An administrator of these tests is curious about how much time people spend on the test. They take an SRS (simple random sample) of 15 test results and find that the times are strongly skewed to the left with a mean of x=14.2 minutes. There are also a few outliers in the sample data. Which conditions for constructing a t interval have been met?
Random/Independent
Find the value for t given n = 18 for the 99% confidence interval for the mean
What is 2.898
A market analyst is curious what proportion of Los Angeles residents have a landline telephone. A survey of 200 randomly selected Los Angeles residents shows that 48% of those selected have a landline telephone. The analyst wants to use this data to construct a one-sample z interval for a proportion.
Which conditions for constructing this confidence interval did their sample meet?
All
Which of the following would make the ME decrease?
a) Increasing sample size
b) Decreasing sample size
c) Increasing Confidence Level
d) Decreasing Confidence Level
e) Decrease sample mean
f) Decrease sample sd
a, d, f
Find the exact value for t with n=73 and a confidence level of 92.5%
-1.8066
Amy works for a company that produces plastic lids and cups for restaurants. She wants to estimate what proportion of lids produced in a day have a defect that makes them not fit the cups. She takes a random sample of 250 lids from the more than 10,000 total lids produced that day and finds 15 lids in the sample with this defect.
Based on this sample, what is the 99% confidence interval for the proportion of lids produced that day with this defect?
(0.021, 0.099)
Camila is curious about the average length of the female blue whales her organization monitors. She takes a random sample of 4 female blue whales from this population. Their average recorded length is x=78 and their standard deviation is sx=10. The distribution of lengths in the sample is roughly symmetric with no obvious outliers.
Based on this sample, create a 95% confidence interval for the mean length (in meters) of female blue whales
(62.09,93.91)
What proportion of scores in a t-distribution with 6 degrees of freedom are above t = 2.447?
.025
Angela wants to use a one-sample z interval to estimate what proportion of employees at her large corporation are satisfied with their benefits. She plans on using a confidence level of 90% and she wants her margin of error to be no more than ± 5%.
What is the smallest sample size required to obtain the desired margin of error?
271
A random sample of 22 people resulted in a 87% confidence interval of (5.8, 12.2). What was the sample sd?
sx = 9.5244
Rank these in order from lowest area to highest (NO CALCULATOR!!!):
a) P(t > 2.1) with df = 19
b) P(t > 2.1) with df = 49
c) P(t < -2.1) with df = 24
d) P(t > -2.1) with df = 199
e) P(z > 2.1)
e, b, c, a, d