Download Review - McNelis

Review
Statistic
Parameter
Test Statistic:
Generic Form:
Confidence Interval:
Generic Form:
What are assumptions used for? To check for what?
Remembering back to Ch. 1….
What’s the formula for a Z-score when talking about averages?
I have an observation that has a Z-score of 1.4. What does this mean about the observation
compared to its mean?
40 year old females have heights that are N(65, 2.5). What percent of females are 66” or
above? Don’t forget notation!
1. Suppose the average (mean) price of gas in a large city is $1.80 per gallon with a standard
deviation of $0.05.
a. Convert $1.90 and $1.65 to z-scores.
b. Convert the following z-scores back into actual values: 1.85 and –1.60.
2. Suppose the attendance at movie theater averages 780 with a standard deviation of 40.
a. An attendance of 835 equals a z-score of:
b. A z-score of –2.15 corresponds to an attendance of:
3. A packing machine is set to fill a cardboard box with a mean of 16.1 ounces of cereal. Suppose the
amounts per box form a normal distribution with a standard deviation equal to 0.04 ounce.
a. What percentage of the boxes will end up with at least 1 pound of cereal?
b. Ten percent of the boxes will contain less than what number of ounces?
c. Eighty percent of the boxes will contain more than what number of ounces?
d. The middle 90% of the boxes will be between what two weights?
4. The life expectancy of wood bats is normally distributed with a mean of 60 days and a standard
deviation of 17 days.
a. What is the probability that a randomly chosen bat will last at least 60 days?
b. What percentage of bats will last between 40 and 80 days?
c. What is the probability that a bat will break during the first month?
 In the problems above, you were always given _________ and ________
and not ________.

However in statistics, we always make conclusions from _________________.

When we have a sample, we don’t have µ and σ anymore,
we have ________ and _______.

So if a population has a distribution:
then the sample has a distribution:

Where did we see problems like this before?
Example of what we’ve seen before:
Cola bottles are supposed to be filled with 300mL of soda. However, bottles are usually
normally distributed with an average of 298 mL and a standard deviation of 3mL.
1- What is the distribution of one bottle?
2- What is the probability of selecting one bottle that is less than 295 mL?
3- What is the distribution of a 6-pack?
4- What is the probability of selecting a 6-pack that has an average amount of cola less
than 295 mL?
Ch. 7: The T-Test

This chapter, we are looking to make conclusions about the unknown parameter …

µ is estimated by ________

Since we don’t know µ, then we don’t know ________ either. Why?

σ is estimated by ________

so, if a population has a distribution of N(µ, σ), we can estimate that by:

But what if we take a sample of size n? How does that affect our estimate of the
population?

x =

But we don’t know σ. We estimate σ with ________

Thus, we will estimate σX with:

Once we do this estimation, we can’t use ____________________- Why?

Instead, we will use what is called the ______________________.
=
=
The T-distribution:

Still…

Still…
o If we don’t have a normal population, what do we check?

There is …

Similarities to Standard Normal Curve (used for z scores):
o
o

Big difference from Standard Normal Curve
o
o Why?

How does the sample size affect the t-distribution?
o Degrees of freedom =
o As the degrees of freedom increase...
The One Sample T-Test
Same steps:
1.
2.
3.
4.
5.
Hypotheses:
 Similar to proportion tests:

Except they are about…
Test Statistic:
 Formula: Generic
P-Value:
 Notation:

Calculator Use:
Conclusion:
 Same 2 sentences, except…
Specific:
t Confidence Interval
Formula: generic

t* =

How do we find t*?
Conclusion:
 Same as with z-interval
Assumptions for t-test and t-interval
1.
2.
Some vocab for this chapter…
Robustness…
Specific:
Z test
parameter we
are estimating
pop. std. deviation
sample std. deviation
Test Statistic
Confidence Interval
Distribution: Name
Distribution: Center
Distribution: Spread
Other
Assumptions
t test
AP Statistics
Section 7.1 - t-test for Mean and t-interval for mean
1. Find the values of the t-distribution that bound the middle 90% of the area under the curve for the
distribution with df = 17.
2. A random sample of size 20 is taken from the weights of babies born at Northside Hospital during
the year 1994. A mean of 6.87 lb and a standard deviation of 1.76 lb were found for the sample.
Estimate, with 95% confidence, the mean weight of all babies born in this hospital in 1994. (It is
assumed from past experience that the weights of newborns are normally distributed.)
3. Construct a 99% confidence interval estimate for the mean  using the sample data (assuming a
normal population): x  16.7, n  24, s  2.6 .
4. The EPA wants to show that “the mean carbon monoxide level of air pollution is higher than 4.9.”
Does a random sample of readings (with sample results x  5.1, n  22, s  1.17 ) present
sufficient evidence at the .05 level of significance to support the EPA’s claim? Previous studies
have indicated that such readings have an approximately normal distribution.
5. Calculate the value of t and the P-value and state the decision that would occur for the following
hypothesis test:
H 0 :   32, H a :   32,   .05, n  16, x  32.93, s  3.1
6. Calculate the value of t and the P-value and state the decision that would occur for the following
hypothesis test:
H 0 :   73, H a :   73,   .1, n  12, x  71.46, s  4.1