Vocabulary
What is the process of drawing conclusions about a population on the basis of sample data?
Inference
What percentage of data is greater than a z-score of 2.4?
0.82%
Formula for the margin of error
z*(σ/sqrt(n))
You have a z-score of 2.5 and your alpha level is 0.01. Can you reject the null hypothesis if it is a two-tailed test?
No, p=0.0124, which is greater than 0.01
You want to know something about the citizens of Eugene of all ages. You conduct a survey by posting a poll on Instagram, and you receive answers from primarily people under 50. What bias is this demonstrating?
Undercoverage.
People over 50 are less likely to see the Instagram poll, so you are excluding a section of the population.
What is a parameter?
A numerical characteristic of a population, such as the population mean or population standard deviation
Suppose that blood sugar levels are normally distributed with a mean of 100 mg/dl (milligrams per deciliter) and a standard deviation of 10mg/dl. David has a blood sugar level of 85 mg/dl. Calculate David's z-score.
z=-1.5
What is the upper limit of a 90% confidence interval of the trunk length of elephants if a study of 100 elephants has a sample mean of x̄=7ft with a standard deviation of σ=1ft
7.1645 feet
Test scores are normally distributed with a mean of 85% and a standard deviation of 5.4%. You believe people who went to tutoring did significantly better. 100 kids went to tutoring, and their mean score was 89.7%. Write out the null and alternative hypotheses.
Ho: µ=85
Ha: µ>85
You want to know how long it takes people to complete an assignment for a WR121 class. You survey 30 people currently taking the class, and find the average time to be 5 hours, with a standard deviation of 1.3. What symbol would we use for the 1.3?
s
You took a sample, so it is a sample standard deviation, which we denote with s.
What is the set of all possible outcomes called?
Sample Space of a random phenomenon
What is the maximum weight a pumpkin can be and still be in the lower 16% of the weight of all pumpkins if the weight of pumpkins is normally distributed with μ=100 and σ=25lb.
75.25lb
Find the confidence interval (in interval notation) with 90% confidence if the standard deviation is 2.3 and the mean of an SRS of 9 is 15.
(13.74 , 16.26)
The time it takes to download a video game is normally distributed with µ=2 hrs and σ=1hr. Dave believes it takes longer than 2 hrs to download a video game and so he randomly downloads 20 video games and finds the average time it takes to download a video game to be 2 hours and 30 minutes. What is the null hypothesis, alternative hypothesis, P-value, and statistical significance of the P-value at a significance level of α=.01
Ho: µ=2hrs,
Ha: µ>2hrs,
P=.0127,
Not statistically significant, and cannot reject the null hypothesis
Find the Least-Squares regression equation for the given information.
xbar=9.42 sx = 0.79
ybar = 14.27 sy = 4.83
r = 0.64
yhat = 3.91x - 22.56
m = 3.91
b = -22.56
What is the difference between one- and two-tailed alternative hypotheses?
One states that a parameter is larger than or smaller than the null hypothesis, and the other states that the parameter is different than the null hypothesis.
The weights of babies are approximately normal with μ = 7.7 pounds and σ = 1.1 pounds, N(7.7, 1.1). What weight would put a newborn baby in the 95th percentile?
9.51 pounds
What is the margin of error for a 90% confidence interval where the mean is 5.4, the standard deviation is 1.1, and the sample is 16 individuals?
0.452
You run an experiment to see if your sample is significantly shorter than the US population. Your sample has a mean height of 65.9in. The population has a mean height of 67.1in and a standard deviation of 2.1in. Is your sample significantly shorter at the 0.05 level? (n=16)
Yes, p=0.0111, therefore it is statistically significant
Using the Empirical rule, estimate the percent of all climbing ropes that have a breaking point of more than 335 pounds, if the breaking point of this certain type of rope is normally distributed with a mean of 330 pounds and a standard deviation of 2.5 pounds.
2.5%