Vocabulary
What is the number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitions in any chance process?
Probability.
A newlywed couple is trying to choose one of two neighborhood supermarkets for their grocery shopping. They decide to randomly select 20 items, check prices at each store, and then conduct a test to determine if one store is significantly less expensive than the other. What test should they conduct?
Matched Pairs
When performing a hypothesis test for a population proportion, researchers obtain a p-value of 0.023. Interpret this p-value
Assuming that the null hypothesis is true, the probability of obtaining the sample statistic or more extreme is 0.023
As sample size increases, what happens to margin of error?
It decreases
What’s the difference between a sample T test and a sample Z test?
A Z-test is used to test a null hypothesis if the population variance is known or if the sample size is larger than 30. A T test is used when the sample size is less than 30 and the population variance is unknown.
What is the law of large numbers?
If we observe more and more repetitions of any chance process, the proportion of times that a specific outcome occurs approaches its probability.
What is the p-value for a z-score of -2.57?
0.0051
A contact lens wearer read that the producer of a new contact lens boasts that their lenses are cheaper than contact lenses from another popular company. She collected some data then tested the null hypothesis. H0: μold-μnew=0 against the alternative Ha: μold-μnew>0. What would the type II error be?
Deciding that the new lenses are not really cheaper, when in fact they are
A researcher is wanting to estimate the population proportion for the number of female lions amongst all lions in South Africa. To estimate this, she takes a random sample of 800 lions and finds that 502 of them are female. Which inference procedure would be best to estimate the true proportion of female lions in South Africa?
What is the best statistic?
Unbiased and lowest variability
What is the probability model?
At a manmade lake in central Pennsylvania, an average of 50 gallons of water flows over the spillway every minute with a standard deviation of 15 gallons. Distribution assumed to be normal. What is the probability that for any randomly chosen minute, fewer than 20 gallons of water goes over the spillway?
0.0228
A New York Times/CBS News Poll asked a random sample of U.S. adults the question “Do you favor an amendment to the Constitution that would permit organized prayer in public schools?” Based on this poll, the 95% confidence interval for the population proportion who favor such an amendment is (0.63, 0.69). What is the point estimate and the margin of error?
Point estimate= 0.63+0.69/2=0.66
The margin of error is +/- 3 percentage points, since the width of the interval is 6 percentage points.
A volunteer for a mayoral candidate's campaign periodically conducts polls to estimate the proportion of people in the city who are planning to vote for this candidate in the upcoming election. Two weeks before the election, the volunteer plans to double the sample size in the polls. The main purpose for this is to?
decrease the standard deviation of the sampling distribution of the sample proportion.
A city planner wants to estimate the proportion of city residents who commute to work by subway each day. A random sample of 30 city residents was selected, and 28 of those selected indicated that they rode the subway to work. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal?
The number of successes (people who ride the subway) is greater than or equal to 10. However, because the number of failures, i.e., the number of people who did not ride the subway (2), is less than 10, the conditions for normality are not met.
What rule states that P(A^c)=1-P(A), where A^C is the complement of event A; that is, the event that A does not occur.
Complement rule.
What is the area under any given density curve, namely the normal distribution?
0.5
Latoya wants to estimate the proportion of the seniors at her boarding school who like the cafeteria food. She interviews an SRS of 50 of the 175 seniors and finds that 14 think the cafeteria food is good. Check whether each of the conditions are met for calculating a confidence interval for the population proportion p.
Random: Latoya selected an SRS of 175 students
10%: Not met because the sample size of 50 is not more than 10% of the population of seniors in the dormitory
Large counts: np̂= 50(14/50)14≥10%
n(1-p̂)=36≥10
What is the Central Limit Theorem?
The central limit theorem says that the sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough
What is the probability that a randomly chosen subject completes at least 3 puzzles in the five minute period while listening to soothing music?
P(x≥3)=.3+.1=0.4
What setting do we use when we perform n independent trials of the same chance process and count the number of times that a particular outcome(called a "success") occurs. Also state the four conditions that this setting uses.
A binomial setting; the four conditions needed are binary, independent, number, and same probability.
A no appointment hair cutter advertises an average wait time of 15 minutes for customers. Customers have claimed that the actual wait time is 30 minutes. A random sample of 30 customers was selected and wait times recorded to determine the true wait time. The power of the test is 50%, how do you increase the power?
Increase sample size and alpha level
According to a recent Pew Research Center report, many American adults have made money by selling something online. In a random sample of 4579 American adults, 914 reported that they earned money by selling something online in the previous year.Assume the conditions for inference are met. Determine the critical value z* for a 98% confidence interval for a proportion.
invNorm(area: 0.01, mean:0, SD:1)= -2.326
A fair coin is to be flipped five times. The first 4 flips land "heads" up. What is the probability of "heads" on the next (5th) flip of this coin?
1/2
Julie generates a sample of 20 random integers between zero and nine inclusive.She records the number of 6's in the sample. She repeats this process 99 more times, recording the number of 6's in each sample. What kind of distribution has she simulated with n and p?
The binomial distribution with n= 20 and p= 0.1