Confidence is Key
This interval estimate gives a range of likely values for a population mean based on a sample mean and margin of error.
What is a confidence interval?
This term describes how many standard deviations a data point is from the mean.
What is a Z-score?
The Grinch's pile of bags filled with stolen ornaments looks a lot like this proper distribution used for inference of means.
With an α level of .05 and a p-value of .0437, this is the conclusion one draws concerning the null hypothesis.
What is rejecting the null hypothesis?
This test is conducted when constructing a confidence interval for one population mean.
What is a 1-sample t-interval for a population mean.
We are 95% confident that the interval (3.256, 7.425) contains the true mean difference between two population means. This is the conclusion that can be drawn from this interval in regards to the population means.
What is, “There is convincing evidence that the population means are different?” (wording may vary slightly)
The margin of error in a Z-interval increases as this value increases.
What is the confidence level
This is how the Grinch's confidence interval for the true average number of ornaments broken in each house changed when he increased the confidence level.
What is wider?
This condition ensures that the sample is representative of the population.
What is random sampling?
T distributions take into account this measure of variability, differentiating them from the normal distribution.
What is degrees of freedom?
This is the 95% confidence interval for a sample of 40 students with a mean test score of 82 and a known population standard deviation of 10.
What is (78.901,85.099)?
If a Z-interval for the mean is (48.2, 51.6), you can be 95% confident this interval contains this quantity.
What is the true population mean?
These are the Grinch's hypotheses for the test he conducts on the average time he spends ransacking each house with the original claim that he's in and out in 5 minutes or less.
What are
H0: μ ≤5
and
Ha: μ > 5?
An experiment is conducted to test if a new teaching method improves test scores. A sample of 40 students is randomly assigned to the new method, and another 40 students are assigned to the traditional method. The sample means are 82 for the treatment group and 78 for the control group. The standard deviations are 5 for both groups. These are the conditions for inference checked to test if there is a significant difference in test scores at the 0.05 significance level.
What are:
Random Assignment
Independence (10% condition)
Approximately Normally Distributed (N>30)?
The t-distribution more closely resembles the Normal distribution as this happens.
What is an increase in degrees of freedom?
You want to know the average height of all the people in ninth grade at a high school. You randomly sample 75 of the 300 students in ninth grade and find the mean height to be 162 cm. This is the 95% confidence interval (rounded to the nearest cm) for the true average height of ninth graders with a standard deviation of 9 cm.
What is (160, 164)?
A nutritionist claims that the average daily protein intake for a specific population is 72 grams. To test this claim, a researcher collects a random sample of 100 individuals and finds that their average protein intake is 74.5 grams. The population standard deviation is known to be 10 grams.What is the P-value
What is p-value = 0.0124
This is the 95% confidence interval for the true average heart growth of Grinch-types if The Grinch's heart grew 2.8 sizes on average with a standard deviation of 0.6 after returning presents to 10 houses, assuming all conditions are met.
What is (2.428, 3.171)?
A battery manufacturer claims their batteries last 100 hours on average. A sample of 25 batteries lasts an average of 98.5 hours with a sample standard deviation of 4 hours. Testing the claim at the 0.01 significance level, this is the test-statistic.
What is t=−1.875?
This test is used to compare the means of 2 related things from the same individuals.
What is a paired t-test?
What is when sampling many many times, 99% of the constructed confidence intervals will capture the true mean?
A researcher wants to estimate the mean weight of a product within 2 units at 99% confidence. The population standard deviation is 10. What minimum sample size is needed?
What is n≈166
The Whos in Whoville surveyed 40 residents on how grumpy Mr. Grinch seemed this year. The average grumpiness rating was 6.2 out of 10, with a known population standard deviation of 1.5. This is the 95% confidence interval for true mean grumpiness.
What is (5.735, 6.664)?
A sample of 50 customers gives a company a mean satisfaction of 4.1 out of 5. The standard deviation of the reviews is 0.6. The restaurant claims that their true mean satisfaction rating is 4.3. Using a 0.01 alpha value, this is the p-value.
What is p ≈ 0.0092?
A researcher wants to know if a new teaching affects test scores. She randomly assigns 40 students to use the new method and compares their average test score to the national average of 75, although the national data did not include a standard deviation. This is the test that should be used.
What is a one-sample t-test?