Definitions
Best estimate to a population proportion
Sample Proportion
What does
\bar x
refer to?
Sample mean
Z score for 95% CI
1.96
What is the best estimate for the population mean?
Sample mean
When writing a null hypothesis, the symbolic statement always includes __________.
An equality (=)
This is added and subtracted from the sample mean in order to construct a confidence interval
Margin of Error
For proportions, how are p and q related?
q = 1-p
If the mean of a sample is 2.3 and the margin of error is 1.5, what is the confidence interval?
(.8,3.8)
How will using a larger sample size affect your spread in the distribution of sample means?
It will lead to a smaller spread in the distribution
If a p-value is 0.03 and the significance level is 0.05, the decision about the null hypothesis is this.
We reject the null hypothesis
The set of all values of the test statistic that causes us to reject the null hypothesis.
The critical region
In a survey of 1035 US adults, 745 say they want to play pickleball regularly. What is
\hat p
?
0.72
What is the margin of error for a sample with a critical value of 1.76, a sample size of 64, and a sample proportion of .33?
0.103
The Central Limit Theorem is particularly useful for making inferences about populations when the population distribution is not normal. Name one type of non-normal distribution.
uniform, exponential, skewed, bimodal, etc.
Rejecting a true null hypothesis is called _________ .
A type I error
The symbol commonly used to refer to significance level
alpha
A student scores 85 on a test with a mean of 70 and a standard deviation of 10. Calculate the z-score for this test score.
1.5
Z score for 99% CI
2.58
You collect a random sample of 25 exam scores from a population with a known standard deviation of 10. What is the standard deviation of the sampling distribution of the mean?
2
In a test of proportions, the null hypothesis states that 40% of people prefer tea over coffee. In a sample of 200 people, 100 prefer tea. Calculate the test statistic.
z = 2.88
How does one find the error to confidence intervals that use the sample proportion as their point estimate?
Error = z score *(sqrt of phat times q hat all over n)
Suppose the mean number of hours a college student sleeps at night is 7 hours with a standard deviation of 1.2 hours. If we take a sample of 49 students, what is the probability that the mean number of hours of sleep the students in the sample get is less than 6.5 hours?
0.002
The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are random variables that follow a normal distribution with a standard deviation of 0.4 m. Determine the interval of 95% confidence for the average heights of the population.
(1.7108, 1.7892)
In a sample of 200 people entering a store, 78 make a purchase. What is the standard deviation of the sampling distribution of the proportion?
0.034
In a test of proportions, the null hypothesis states p=0.6. A sample of n=100 results in a sample proportion (p-hat) = 0.65. Find the p-value for a two-tailed test.
p = 0.307