Means
When the population standard deviation is unknown, you should use this table.
T-table
If we want to see if there is a difference between the proportion of seniors who eat in the dining hall and the proportion of freshmen who eat in the dining hall, we should run this test.
2 proportion z test
Is political affiliation related to the month that the person was born in? 3000 voters were studied.
Chi-Square Test for Independence
This is the type of test we should run when we are looking at the distribution of categorical variables
Chi square GOF
Solve for x
40x + 30 = 20 - 10x
x = -0.20
If we are going to compare the average weight of a sample of 100 bags of m&ms to the advertised average (12.0 oz), we should run this type of test.
What is a t test
We want to see if there is a difference between the proportion of seniors who eat in the dining hall and the proportion of freshmen who eat in the dining hall. What is our null hypothesis (use plain english)?
There is no difference between the proportion of seniors and the proportion of freshmen who eat in the dining hall.
Are male swimmers faster than female swimmers? 40 men and 30 women were selected at random to swim in a 100-meter race.
Hyp. Test for the Difference Between 2 Means
What is our degrees of freedom is we have 5 columns and 3 rows in our table (chi square test for independence)?
8
Calculate the standard deviation of p hat if:
p = 0.34
n = 400
.0237
You are curious about the average number of hours that Asheville School students sleep each night. What inference method should you use?
What is a t interval
We want to see if there is a difference between the proportion of seniors who eat in the dining hall and the proportion of freshmen who eat in the dining hall, we run a test, and calculate a p value of .08. What can we conclude (in context).
We cannot reject the null hypothesis, because .08 > .05. There is not sufficient evidence to conclude that there is a difference between the proportion of freshman and the proportion of seniors who eat in the dining hall.
You want to estimate the average number of texts that college students send each day. You survey 150 college students.
Confidence interval for mean (t interval)
How do you calculate expected counts for a chi square test for independence?
Row total times column total divided by total total.
What is the margin of error for the confidence interval (0.55, 0.72)
.085
We want to see if there is a difference between the proportion of seniors who eat in the dining hall and the proportion of all students who eat in the dining hall. It is known that 80% of all students eat dinner in the dining hall. We sample 55 seniors, and find that 38 eat in the dining hall. What would a type 1 error be in context of this question?
We conclude that there is a difference between the proportion of seniors who eat in the dining hall and the proportion of all students who eat in the dining hall, when in fact there is no difference.
Typically, your shop has 140 customers per day. Over the last thirty days you have a special advertisement in the Daily Tribune. You chart your daily number of customers. Is this ad effective?
Hypothesis Test for a Population Mean (t test)
If we are running a chi square test for association to see if there is a difference between men and women with regards to their favorability rating for a new movie, what should our null hypothesis be?
There is no association between gender and favorability rating for the movie in question.
Consider the weights of 18 month old boys in the U.S. According to published growth charts, the average weight is approximately 11.8 kg with standard deviation of 1.28 kg. Calculate the percentage of 18 month old boys in the U.S. who weigh between 10.5 kg and 14.4 kg.
0.9788 - 0.1539
= 0.8249
Pepsi claims that bubly has 12.0 oz in each can with a standard deviation of 0.1 oz. You take a random sample of 65 bubly cans, and measure the amount of water in each can. You then take the average of the cans in your sample. You find that the average of the cans in your sample is 11.95 oz. Is Pepsi underfilling their cans? What can you conclude (use p value in order to get credit)?
Reject null hypothesis, p = 2.777 x10 ^ -5
We want to see if there is a difference between the proportion of seniors who eat in the dining hall and the proportion of all students who eat in the dining hall. It is known that 80% of all students eat dinner in the dining hall. We sample 55 seniors, and find that 38 eat in the dining hall. Calculate the p value and draw a conclusion.
We can conclude that there is a difference between the proportion of seniors who eat in the dining hall and the proportion of all students who eat in the dining hall.
The US Census bureau recently came out with the percents of Americans who are working in Service industry, Manufacturing, Unemployed and Other. A researcher wants to find out if these percents are different in South Lake Tahoe. 100 people were surveyed.
Chi Square GOF
A professor thinks that 60% of his students will purchase his book, 25% will print it from the web, and 15% will read it online. At the end of the semester, he asks his class to complete a survey to indicate what format of the book they used. Of the 126 respondents, he finds that 71 bought the book, 30 printed from the web, and 25 read it online. Run a chi squared GOF test and calculate the p-value.
0.313
The probability of a type 1 error is .05, and the probability of a type 2 error is .10. The probability of a type 1 error then goes up to .10, and the probability of a type 2 error goes down to .05
Calculate the "power" in this new scenario.
0.95 (1-.05)