The Normal Curve
Margin of Error
Difference of Means
Potpourri
100
This is the shape of the normal distribution.
Bell - shaped
100
A survey of Mr. Kennedy's students from a random sample found that 50% of them would vote for him for president, with a margin of error of 5%. What is the range of values you expect the true proportion of students who would vote for him to be within?
45% to 55%
100
A group of 50 students were randomly divided into two groups. Group 1 took a statistics test with no music, and group 2 took the same test while listening to Vivaldi's The Four Seasons. The mean score for group 1 was 78, and the mean score for group 2 was 81. Find the difference of means between the two groups.
3 points
100
Which US State houses the Liberty Bell?
Pennsylvania
200
This is the mean and standard deviation of the normal distribution, respectively.
0 and 1
200
A sample from a local restaurant estimated the mean wait time to be 20 minutes and standard deviation of 6 minutes on a busy Saturday night. Several other Saturday nights were sampled as well. The mean of mean wait times from these samples was 21 minutes and the standard deviation of means was 2 minutes. Estimate the population mean wait time and provide a margin of error you expect 95% of sample means to be within.
21 +/- 4 minutes.
200
The results of a randomized simulation conclude that the mean difference of means is 0.05 with a standard deviation of 0.5. The observed difference between the control and treatment group was 1.2. Is the observed difference likely explained by random chance alone?
No, it is likely due to the treatment since it is further than two standard deviations from the mean difference of means.
200
Name the three principal Axis Powers during World War 2.
Germany, Italy, Japan
300
This is the area under the curve to the left of the critical value - 1.
0.1587
300
Describe one way we have found a margin of error for a sample statistic.
Simulated multiple samples to find the standard deviation of the sampling distribution.
300
Determine if the observed difference of means of 3.4 is likely due to a treatment:
Yes
300
Mt. Kilimanjaro is located in this East African country.
Tanzania
400
Male height in the United States is normally distributed with a mean of 70 inches and a standard deviation of 3 inches. Determine the z-score of a an individual that is 5 ft. 8 in.
-2/3
400
A May Survey from the UNH Survey Center found the 44% of likely voters from NH would vote for Joe Biden in the 2024 general election if held today, with a margin of error of +/- 2.8%. In the same survey, 41% of voters would vote for Trump if elections were held today. The report says they are statistically tied. Why is Biden not a clear winner according to this poll?
The ranges of values in which we expect the true population proportions to be in overlap, thus, we can not conclude that Biden is definitively ahead of Trump. It is possible the true populations are such that Trump is ahead, given this margin of error.
400
How do we know if a difference of means between two samples is likely due to random variation, or from a treatment?
Estimate the probability that a difference at least as extreme as that which occurred between the control and the treatment groups could result from random variation alone.
400
Machu Picchu is the famed terraced city constructed by this ancient civilization.
Inca
500
Male height in the United States is normally distributed with a mean of 70 inches and a standard deviation of 3 inches. Determine the probability that a randomly selected American male is greater than 6 feet tall.
25%
500
Define Margin of Error... be precise
The maximum expected difference between a sample statistic and the true population value.
500
The following data were obtained from an experimental study:
Group 1: 16 16 14 13 17 14 17 13 18 13
Group 2: 17 16 13 14 18 13 13 18 13 18
Using a difference of means simulator, determine if the difference of means is likely due to a treatment or random variability. Back up your argument by finding the probability, within your simulation, that a result at least as extreme occurred from random chance alone.
Answers vary, but not difference is likely due to random variation.
500
What led to the Pine Tree Riot of 1772 in Weare, NH?
The King of England prohibited colonists from cutting down Pine Trees big enough to be used for masts in the Royal Navy. A search of NH sawmills and the discovery of trees marked for the crown precipitated this particular riot.