Vocab
define a statistic
the number that describes a
sample
A ketchup company regularly receives large shipments of tomatoes. For each shipment that is received, a supervisor takes a random sample of tomatoes to see what percent of the sample is bruised and performs a significance test. If the sample shows convincing evidence that more than 25% of the entire shipment of tomatoes is bruised, then they will request a new shipment of tomatoes. What kind of test is this?
One-sample proportion test
A study is done that determines the length of geckos to be normally distributed with µ=7in Amanda believes the mean length of geckos is less than 7in and conducts her own study where she randomly measures 10 geckos and finds their mean length to be 6.3 inches and sample standard deviation to be s=1.1in. She conducts her study using a significance level of α=.05
t=2.01>1.833, so it is significant and you reject the null hypothesis
If a researcher wants to estimate the average height of adult males in a population with a known standard deviation of 3.4", and they collect a sample of 100 men with an average height of 5'9", estimate the true population mean with 99% accuracy.
[68.12, 69.88]
Suppose we know that a t-statistic of 1.56 with 23 degrees of freedom gives a one-sided P -value of .0662. Then a t-statistic of 2.23 with 23 degrees of freedom would give a (bigger/smaller/the same) one-sided P-value
smaller one-sided P-value
if an individual might respond in a way that makes them look good it is ____ bias
response
Amelie has balloons from two different brands. She wants to test the durability of each brand by measuring the volume of water that can be pumped into the balloons before they burst. Brand A had 8 balloons that averaged 10.2L with a standard deviation of 1.2L. Brand B had 8 balloons that averaged 11.8L with a standard deviation of 0.9L. Amelie wants to determine if the mean volumes of the two brands are significantly different. What kind of test is this?
two-sample t test
Your friend claims that she is better than you at rock-paper-scissors, and can win more than the expected 1/3 of the time. You play 30 rounds together and she wins 14 times. We want to decide whether this is statistically significant evidence, at the .025 level, that her claim is true.
z=1.71 (use +4 rule), p=.0436, so it is not significant and we fail to reject the null
A biologist surveyed an SRS of 22 lizards in a certain region and found that 13 of them had spots. Using the plus-four method to find a 97% confidence interval for the proportion of lizards in this region that have spots.
[0.3668, 0.7872]
If we fail to reject H0 when in fact Ha is true,
this is a...
type II error
Assign workers to an assembly line moving at a fixed pace or to a self-paced setting. All subjects work on both lines in random order. After two weeks on each line, workers take a job satisfaction test. What kind of design is this?
matched pairs design
A study tried to determine if more than half of a sample of people thought the dress was white and gold as opposed to blue and back. The study found that out of the 10,000 people they surveyed 4741 people thought the dress was black and blue. Did more people think that the dress was white and gold at the 0.01 significance level?
z=5.18, p<0.00001, so it is significant and you reject the null
Do more husbands cheat on their wives more than wives cheat on their husbands ("Statistics brain," 2013)? Suppose you take a group of 1000 randomly selected husbands and find that 231 had cheated on their wives. Suppose in a group of 1200 randomly selected wives, 176 cheated on their husbands. Estimate the difference in the proportion of husbands and wives who cheat on their spouses using a 95% confidence level.
CI= [0.0513, 0.1173]
the difference between an observed value of the response variable and the value predicted by the regression line
residual
Two types of valves are being tested to determine if there is a difference in pressure tolerances. Fifteen out of a random sample of 100 of Valve A cracked under 4,500 psi. Six out of a random sample of 100 of Valve B cracked under 4,500 psi. Test at a 5% level of significance. What kind of test is this?
2 proportion test
A city has 8 traffic circles (roundabouts) and 253 stoplights at what it deems “major intersections.” It measures the number of crashes per 100,000 vehicles passing through each intersection, finding that the traffic circles have an average of 4.3 crashes per 10,000 vehicles and a standard deviation of 2.9, while the stoplights have an average of 5 crashes per 10,000 vehicles and a standard deviation of 3.7. We want to decide whether this is statistically significant evidence that traffic circles are safer than stoplights at the 0.1 level.
t=-14.89 , p<0.1, there is significant evidence to support this claim
The total rainfall in 2020 at six cities on the Oregon coast had a mean of 71.9 inches and a standard deviation of 10.3 inches. The total at five cities in the Willamette valley had an mean of 39.9 inches and a standard deviation of 2.8 inches. Give a 80% confidence interval for the difference in average rainfall between the coast and the valley.
32 ± 6.617, [25.383, 38.617]
A company that makes marbles claims that 42 percent of their marbles are blue. If you order a random sample of 150 marbles, what is the probability that at least 65 will be blue?
0.37350