Shape, Center, Spread
According to the Central Limit Theorem (CLT), when we take the average of our samples (which is random/independent/and large enough) we should get what type of model?
Normal Model - Narrow, Unimodal, Symmetric
Elisa has data from a random sample of 18 subjects and is constructing a 95% confidence interval for the population mean. How do you find the degrees of freedom, and what are the degrees of freedom for this problem?
df = n - 1 = 17
Congress regulates corporate fuel economy and sets an annual gas milage for cars. A company with a large fleet of cars hopes to meet the 2011 goal of 30.2 mpg or better for their fleet of cars. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 32.12 mpg and a standard deviation of 4.83 mpg. Is this strong evidence that they have attained their fuel economy goal?
Do steps P and H of PHANTOMS
u = mean fuel economy (mpg)
Ho : u = 30.2
Ha : u > 30.2
Using this 98% confidence interval, interpret it if we were finding the average grade of a statistics student in Texas, and sampled different classes across Texas.
(67.89, 78.92)
We are 98% confident that the true average/mean grade of a Texas statistics student is between a 67.89 and a 78.92.
When do we use a t-model in hypothesis tests or confidence intervals?
Answer: When we are working with ______ and the _________ standard deviation is unknown.
Means ; Population
When we are working with means and population standard deviation is unknown.
The National Health Survey suggested that heights of women have a mean of 65 inches and a standard deviation of 3.5 inches. Describe the shape of the sampling distribution model of mean heights of 100 randomly chosen women.
Shape: Unimodel, mostly symmetric, mostly NORMAL.
Elisa has data from a random sample of 18 subjects and is constructing a 95% confidence interval for the population mean. What is the value of t*?
df = n - 1 = 17
2.11
Congress regulates corporate fuel economy and sets an annual gas milage for cars. A company with a large fleet of cars hopes to meet the 2011 goal of 30.2 mpg or better for their fleet of cars. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 32.12 mpg and a standard deviation of 4.83 mpg. Is this strong evidence that they have attained their fuel economy goal?
Do steps A and N of PHANTOMS
Independent and Random
50 < 10% of all company trips
50 >= 25
One- Sample T-Test
Using this 98% confidence interval, where we are finding the average grade of a statistics student in Texas, and sampled different classes across Texas, could we say that all statistics students are passing their statistics classes?
(67.89, 78.92)
Hint: There are two reasons for the answer, must say both.
NO. For one, we are never 100% about everyone in statistics (it uses all in the question). Another thing, part of the confidence interval lies below the passing grade of a 70.
The National Health Survey suggested that heights of women have a mean of 65 inches and a standard deviation of 3.5 inches. Describe the center of the sampling distribution model of mean heights of 100 randomly chosen women.
Center: the mean - 65 inches
The housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 41 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss to be $9560 with a standard deviation of $1500.
Find the value of t* for this problem. (using 95% confidence interval)
t* = 2.021
Congress regulates corporate fuel economy and sets an annual gas milage for cars. A company with a large fleet of cars hopes to meet the 2011 goal of 30.2 mpg or better for their fleet of cars. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 32.12 mpg and a standard deviation of 4.83 mpg. Is this strong evidence that they have attained their fuel economy goal?
Do steps T and O of PHANTOMS (HAVE TO WRITE FORMULA AND PLUG IN)
t = (32.12 - 30.2)/(4.83/sqrt(50))
p-value = .004
A marketing company reviewing the length of radio ads monitored a random sample of ads over several days. They found that a 95% confidence interval for the mean length (in seconds) of ads aired daily was (38, 47). Interpret the interval.
We are 95% confident that the true mean length of ads aired daily was between 38 and 47 seconds.
The National Health Survey suggested that heights of women have a mean of 65 inches and a standard deviation of 3.5 inches. Describe the spread of the sampling distribution model of mean heights of 100 randomly chosen women.
Spread: population std. dev. = sample std. dev. / sqrt(n)
so, 3.5 / sqrt(100)
The housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 41 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss to be $9560 with a standard deviation of $1500.
Calculate the 95% confidence interval. (HAVE TO WRITE EQUATION AND PLUG IN)
FORMULA: x-bar = 9560, Sx = 1500, n = 41
(9086.5 , 10033)
Congress regulates corporate fuel economy and sets an annual gas milage for cars. A company with a large fleet of cars hopes to meet the 2011 goal of 30.2 mpg or better for their fleet of cars. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 32.12 mpg and a standard deviation of 4.83 mpg. Is this strong evidence that they have attained their fuel economy goal?
Do steps M and S of PHANTOMS
Reject the null
We have strong evidence that the mean fuel economy is above 30.2 MPG.
A researcher tests whether the mean cholesterol level among those who eat frozen pizza exceeds the value considered to indicate a health risk. She gets a p-value of 0.07. Explain in context what the 7% represents.
There is a ____ % chance that her sampling would have shown a mean cholesterol level _________, when really, it is _______.
There is a __7__ % chance that her sampling would have shown a mean cholesterol level _at a health risk_, when really, it is _at a healthy level_.
The housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 41 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss to be $9560 with a standard deviation of $1500.
Interpret the 95% confidence interval.
(9086.5 , 10033)
We are 95% confident that the true average loss in home value is between $9,086.5 and $10,033.
Congress regulates corporate fuel economy and sets an annual gas milage for cars. A company with a large fleet of cars hopes to meet the 2011 goal of 30.2 mpg or better for their fleet of cars. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 32.12 mpg and a standard deviation of 4.83 mpg. Is this strong evidence that they have attained their fuel economy goal?
Answer the question (In a complete sentence)
Yes. We found strong evidence that the mean fuel economy is above 30.2 MPG, thus we found evidence they reached their 2011 goal of having a fuel economy of 30.2 MPG or better.
The housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 41 bids from potential buyers to estimate the average loss in home value. They want to know if the loss has increased since 2008. They calculate and get a p-value of .23. Explain in context what the 23 % represents.
There is a ____ % chance that the sample would have shown a mean loss of house value _________, when really, it is _______.
There is a _23_ % chance that the sample would have shown a mean loss of house value _better than it was in 2008_, when really, it is _not better than it was in 2008_.