Definitions
A number that describes a population.
Parameter
Of the mean, median, and mode, which must be a value that actually appears in the data set?
Mode
x | 0 | 5 | 10 | 15 |
P | 0.15 | 0.26 | 0.41 | 0.18 |
What is P(More than 5)?
0.59
If P= 0.03, would the result be statistically significant at the a = 0.05 level? What about a = 0.01?
A poll is conducted of 3500 households close to major national airports and another 2000 that are not close to an airport, in order to study whether living in a noisier environment results in health effects. Is this a randomized experiment or an observational study?
Observational study
A subset of an entire collection of individuals, containing the individuals that are actually observed.
Sample
Calculate the mean, median, and mode of this sample: 550 700 420 580 550 450 690 390 350
Mean: 520; median: 550; mode: 550
What are the following conditions for:
1. A fixed # of trials are conducted.
2. There are two possible outcomes for each trial (Success/failure).
3. The probability of success is the same on each trial.
4. Trials are independent.
5. The random variable X represents the number of successes that occur.
Binomial Distribution
Find the critical value.
H0: µ=4 versus H1: µ > 4, n=25, a=0.05.invT (1-0.05, 25)= 1.71
Find the degrees of freedom given:
n = 24
n=3
df= 3-1=2
This states that 68% of the data is within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3.
Empirical Rule
Compute a five-number summary for the following set of data:
37 17 26 24 32 19 20 31 29 33 20
Min: 17 Q1: 20 Med: 26 Q3: 32 Max: 37
17, 20, 26, 32, 37
A study shows that the mean number of hours spent studying for tests throughout the year is 38 with a standard deviation of 4 hours. What proportion of people study for more than 43 hours?
0.1056
A test is made of H0: μ=63 versus H1: μ >63. The true value of µ is 75, and H0 is not rejected. Is this a Type I error, a Type II error, or a correct decision?
Type II Error
Find the sample variance and standard deviation of the following sample:
22 27 13 53 47 50
s= 16.789
s2= 281.9
The probability of observing a value for the test statistic that is as extreme as or more extreme than the value actually observed, under the assumption that the null hypothesis is true.
P-Value
Records at a hospital show that a certain surgical procedure takes an average of 162.8 minutes with a standard deviation of 4.9 minutes. If the data are approximately bell-shaped, between what two values will about 95% of the data fall?
153 and 172.6
A person pays $700 a year for car insurance. If this person gets in an accident within the first year, the car insurance will pay them $8,000. The probability that a person gets in a car accident in that first year is 0.05. Let X be the profit made by the insurance company. Find the expected value of the profit.
0.05(-7300) + 0.95(700) = $300
Two methods are being considered to increase production of a paint manufacturing process. In a random sample of 50 days, the mean daily production of using the first method was 645 tons with a standard deviation of 50 tons. In a random sample of 64 days, the mean daily production using the second method was 630 tons with a standard deviation of 40 tons. Create a 95% confidence interval for the difference in mean daily production between the two methods.
2-SampTInt
(-2.20, 32.20)
How do you find the standard error?
population std. dev / square root of n
Define Type 1 and Type 2 Errors
Type 1: Reject the null hypothesis when it is true
Type 2: Failing to reject the null hypothesis when it is false
Last semester, Sarah took four courses. She got an A in psychology (4 credits), a B in statistics (5 credits), an A in English (3 credits), and a C in music (2 credits). In her school’s grading system, an A is worth 4 points, a B is worth 3 points, a C is worth 2 points, and a D is worth 1 point. Calculate Sarah's GPA.
3.357
4(4)+5(3)+3(4)+2(2) / 4+5+3+2 = 3.357 OR
L1 enter grades, L2 enter weights(credits), 1-var-stats with freq. set to L2
Lengths of a table are normally distributed. They have a mean of 72 inches with a standard deviation of 2 inches. What length has a z-score of 0.28?
72.56
The General Social Survey polled a sample of 1399 adults in the year 2014, asking them how many hours per week they spent on the internet. The sample mean was 11.62 with a standard deviation of 15.02. A second sample of 1361 adults was taken in the year 2018. For this sample, the mean was 13.84 with a standard deviation of 16.96. Assume these are simple random samples from populations of adults. Use the α = 0.05 level. Compute the test statistic.
2-SampTTest
-3.637
This is the nonparametric two-sample t-test for independent samples.
Rank-Sum Test
(Mann-Whitney)