Normal Distribution
Per this theorem, the sample mean is assumed to be an unbiased estimator of the population mean when n > 30.
What is the Central Limit Theorem?
These conditions must be met in order to use a normal approximation for the binomial distribution.
What is np > 5 and nq > 5?
These are the criteria for using the Student's t Distribution.
What are (1) an unknown population standard deviation and (2) sample size less than 30?
This is the z-critical value associated with a 95% confidence interval.
What is 1.96?
This is a statement of no change, no difference, or no relationship between the objects of a research study.
What is a null hypothesis?
This equation represents the standard deviation of the sampling distribution.
What is σ/√n?
The equation p(1-p)(z/E)2 is used to calculate this.
What is the sample size when a preliminary estimate is known?
This is the number of values that can logically be assumed to be independent within a sample.
What are degrees of freedom?
This is the largest distance between a point estimate and the population mean permitted under a given confidence.
What is the maximal margin of error?
When we reject the null hypothesis even though it is true, we have committed this.
What is a Type I error?
This condition must be met in order to use z-scores and the Standard Normal Distribution.
What is the population standard deviation must be known?
This adjusts the values of a discrete random variable by +/- 0.5 to a continuous random variable.
What is a continuity correction?
Identify the difference in the equations for the z-score and the t-score.
What is the use of s instead of σ?
95% confidence indicates the population mean has a 95% probability of being within the interval (true or false).
What is false?
This is the area under the distribution for which we fail to accept the null hypothesis.
What is the rejection region?
A machine is used to put bolts into boxes. It does so such that the actual number of bolts in a box is normally distributed with a mean of 106 and a standard deviation of 2. Determine the probability that a box selected at random will contain at least 105 bolts.
What is 0.6915 or 69.15%?
z = (105 - 106)/2 = -0.5
(we look for the area to the right)
The equations √(pq/n) this value in a binomial distribution.
What is standard deviation for proportions?
Given a critical value of 2.64 and a test statistic of t=2.5, what conclusion would you draw about the null hypothesis?
What is accept the null hypothesis?
Suppose we want to estimate the average weight of an adult male in Dekalb County, Georgia. We draw a random sample of 1,000 men from a population of 1,000,000 men and weigh them. We find that the average man in our sample weighs 180 pounds, and the standard deviation of the sample is 30 pounds. Given a 95% level of confidence, calculate the maximal margin of error.
What is 1.859?
z95% = 1.96
E = 1.96 * 302/√1000 = 1.859
When the alternate hypothesis predicts a "not equal" relationship between the groups under study, we perform this kind of test.
What is a one-tailed test?
A machine is used to put bolts into boxes. It does so such that the actual number of bolts in a box is normally distributed with a mean of 106 and a standard deviation of 2. A company orders 10 boxes. Determine the probability that all 10 contain at least 105 bolts?
What is 0.9429 or 94.29%?
z = (105 - 106)/(2/√10) = -1.58
These are the steps for calculating a binomial approximation.
What are (1) determining mean and standard deviation; (2) performing a continuity correction; (3) calculating the z-score; (4) finding the associated p-value?
A random sample of 18 adult male wolves from a national park is taken and the mean weight is determined to be 94 lbs with a standard deviation of 5.8 lbs. A wolf is considered malnourished if they weigh less than 70 lbs. Determine the probability that a male wolf weighs 70 lbs or less.
What is 0%?
t = (70 - 94)/(5.8/√18) = -17.55
The local baseball team conducts a study to find the amount spent on refreshments at the ball park. Over the course of the season they gather simple random samples of 50 men and 100 women. For men, the average expenditure was $20, with a standard deviation of $3. For women, it was $15, with a standard deviation of $2. What is the 95% confidence interval for the spending difference between men and women? Assume that the two populations are independent and normally distributed.
What is ($4.08, $5.92)?
z99% = 1.96
E = 1.96*√(32/50 + 22/100) = 0.919
(20-15) - 0.919 < μ < (20-15) + 0.919
A null hypothesis is rejected under these conditions.
What is (1) a p-value LESS than the significance level or (2) a test statistic GREATER than the critical value?