Vocab
A ____ is a number that describes some characteristic of a sample.
Statistic
If you were constructing a CI for proportions, find z* for a 95% confidence level.
1.96
Form a conclusion for the 95% confidence interval, (0.073, 0.124), which represents the proportion of students who were tardy to school.
We are 95% confident that the interval from 0.073 to 0.124 captures the true proportion of all students who are tardy to school.
We want to find the average premiums paid on life insurance policies. So, we take a random sample of 45 life insurance policy holders and calculate the average paid. Determine if the conditions for means have been met.
Random - Yes! "random sample of 45..."
Large - Yes! 45 > 30
When the sample size is increase, the margin of error _________.
DECREASES!
p is used to represent ___________
population proportion
If you were constructing a CI for proportions, find z* for a 97% confidence level.
2.17
A student wants to estimate what proportion of her peers are going into a 2-year program. She takes an SRS of 50 students and found 14 of them plan on enrolling in a 2-year program. Check if the conditions for proportions have been met.
Random - yes! SRS
Large counts - Yes! np=14, n(1-p)=36 >10
How much time do students spend on homework? You collect data from your 20 classmates and calculate the mean amount of time that each student spent on homework. Check if the conditions for means have been met.
Large - NO 20 < 30
Given the interval (15.2, 16.8), find the point estimate and margin of error.
PE = 16, ME = 0.8
The_____ gives the long run success rate of confidence intervals calculated with C% confidence.
Confidence Level C
What critical value t* should be used in constructing a 90% CI for mean when n=30? Round to 3 decimal places.
1.699
Of 367 randomly selected students, 30 said that they planned to work in a rural community. Find a 95% confidence interval for true proportion.
(0.054, 0.110)
A 95% confidence interval for the true mean weight of all packages received by a parcel service was found to be (29.59, 31.61). Write up a conclusion for such interval.
We are 95% confident that the interval 29.59 to 31.61 captures the true mean weight of packages received by the parcel service.
At a swim meet, 8 different swimmers complete in the 800 meter freestyle race. How many different ways are there for these swimmers to finish?
40,320
The _____ of an estimate describes how far, at most, we expect the point estimate to vary from the true population value.
Margin of Error
What critical value t* should be used in constructing a 95% CI for mean when n=85? Round to 3 decimal places.
1.989
In a telephone poll of 1012 adult Americans, 11% of the respondents said that Regan was a great president. Give a 98% confidence interval for the proportion of all adult Americans who think Regan was great.
(0.087, 0.133)
A laboratory tested 83 smoothies from the mega menu at Smoothie Uniiverse and found that the sample mean number of calories was 233 and sx=12.9 ounces. Construct a 95% confidence interval for the true mean of calories of all such smoothies.
(230.183, 235.817)
At the beginning of the chapter, Coach Drown said matching symbols would be on the test. How many did she say would be on the test?
5! (out of a total of 7 that were given)
The ____ is a multiplier that makes the interval wide enough to have the stated capture rate.
Critical Value
What critical value t* should be used in constructing a 98% CI for mean when n=22? Round to 3 decimal places
2.518
A survey of 300 students reveals that 112 favor year round school with two week vacations every ten weeks. Construct a 98% CI for the true proportion of all students who favor year round school. Complete the FULL 4_STEP PROCESS
98% CI for proportion of all students who favor year round.
Random - yes, Large - np=112, n(1-p)=188>10 yes
(0.308, 0.438)
We are 98% confident that the interval 30.8% to 43.8% captures true proportion of students in favor.
A group of 67 randomly selected lifeguards from Orange County, CA have a mean age of 24.6 with a standard deviation of 2.5 years. What is the 90% confidence interval for the mean age of all lifeguards from Orange County? Complete the FULL 4-STEP PROCESS
90% CI for true mean age of OC lifeguards.
Random - yes, Large - 67>30 yes
(24.09, 25.11)
We are 90% confident that the interval 24.09 to 25.11 captures the true mean age of OC lifeguards.
What is Coach Drown's middle name?
Rose