AP Statistics Review
An SRS of size 100 is taken from Population A with proportion 0.8 of successes. An independent SRS of size 400 is taken from Population B with proportion 0.5 of successes. The sampling distribution for the difference (Population A-Population B) in sample proportions has what mean and standard deviation?
mean = 0.3; standard deviation = 0.047
Start here Pg. 548 #3 in peacock book
not sure yet
Which of the following is NOT an assumption of a Binomial Distribution?
All trials are dependent on each other.
Below are dot plots of values taken by three different statistics in 30 samples from the same population. The true value of the population parameter is marked with an arrow.
Statistic C
We calculate the probability of rolling a 6 for the first time on the 6th roll of a die using the binomial distribution?
False
The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean
if the sample size is reasonably large (for any population).
Eleven percent of the products produced by an industrial process over the past several months have failed to conform to specifications. The company modifies the process in an attempt to reduce the rate of nonconformities. In a random sample of 300 items from a trial run, the modified process produces 16 nonconforming items. Find the p-value used to run a significance test in order to determine if the modified process reduced the rate of products that failed to conform to specifications.
0.000789
A researcher initially plans to take an SRS of size n from a population that has mean 80 and standard deviation 20. If he were to double his sample size (to 2n), the standard deviation of the sampling distribution of the sample mean would be multiplied
1 / square root of 2
Some scientists believe that a new drug would benefit about half of all people with a certain blood disorder. To estimate the proportion of patients who would benefit from taking the drug, the scientists will administer it to a random sample of patients who have the blood disorder. What sample size is needed so that the 95% confidence interval will have a margin of error of no more than 3%?
1068
The Department of Health plans to test the lead level in a public park. The park will be closed if the lead level exceeds the allowed limit. Otherwise, the park will be kept open. The department conducts the test using soil samples gathered at randomly selected locations. Which of the following decisions would constitute making a Type I error in this situation?
Closing the park when the average lead level is acceptable.
Resting pulse rate is an important measure of the fitness of a person's cardiovascular system, with a lower rate indicative of greater fitness. The mean pulse rate for all adult males is approximately 72 beats per minute. A random sample of 25 male students currently enrolled in the Agriculture School at a major university was selected and the mean resting pulse rate was found to be 80 beats per minute with a standard deviation of 20 beats per minute. The experimenter wishes to test if the students are less fit, on average, than the general population. The null and alternative hypotheses are
H0: mean = 72 HA: mean is greater than 72
In checking conditions for constructing confidence intervals for a population mean, it's important to plot the distribution of sample data. Below are dot plots describing samples from three different populations. For which of the three samples would it be safe to construct a t-interval?
Sample Y only
The number of undergraduates at Johns Hopkins University is approximately 2000,while the number at Ohio State University is approximately 60,000. At both schools, a simple random sample of about 3% of the undergraduates is taken. Each sample is used to estimate the proportion p of all students at that university who own an iPod. Suppose that, in fact, p = 0.80 at both schools. Which of the following is the best conclusion?
The estimate from Johns Hopkins has more sampling variability than that from Ohio State.
The variability of a statistic is described by
The spread of its sampling distribution
The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The central limit theorem says that
the mean burnout time for a large number of bulbs has a distribution that is close to Normal.
Which of these has a Binomial model?
the number of people in a class of 25 who have taken Statistics
Which of these has a Geometric model?
the number of people we survey until we find someone who has taken Statistics
In a study of the effects of acid rain, a random sample of 100 trees from a particular forest is examined. Forty percent of the trees show some signs of damage. Which of the following statements is correct?
40% is a statistic
In a study of the effects of an ACT prep course, a random sample of 100 high school juniors were chosen to take the course. After the course, 56% of the students improved their ACT scores by at least 3 points. Which of the following statements is correct?
56% is a Statistic
A noted psychic is tested for extrasensory perception. The psychic is presented, one at a time, with cards that are marked with one of four symbols: a star, a cross, a circle, or a square. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Which of the following is the smallest number of trials you would have to conduct to estimate p to within ± 0.01 with 95% confidence? (Use the guess 0.25 as the value for p, since this would be the value of p if the psychic were merely guessing.)
7203
Which one of the following sample data sets would satisfy the Normal/Large sample condition for performing a one-sample t-procedure?
A sample of 38 prices for new houses in Sonoma County, California that is moderately skewed to the right but has no outliers.
A group of nutritionists is hoping to prove that a new soybean compound has more protein per gram than roast beef, which has a mean protein content of 20. A random sample of 5 batches of the soy compound have been tested, producing protein contents of 15, 22, 17, 18, and 23. Which of the following conditions must be met in order to carry out a legitimate statistical test of the nutritionists' claim? I. The observations are from a Normally distributed population. II. The data can be viewed as coming from a simple random sample. III. The standard deviation of the population is known.
I. The observations are from a Normally distributed population. II. The data can be viewed as coming from a simple random sample.
Which of the following distributions has a mean that varies from sample to sample?
II. The distribution of sample data
How much more effective is exercise and drug treatment than drug treatment alone at reducing the rate of heart attacks among men aged 65 and older? To find out, researchers perform a completely randomized experiment involving 1000 healthy males in this age group. Half of the subjects are assigned to receive drug treatment only, while the other half are assigned to exercise regularly and to receive drug treatment. The most appropriate inference method for answering the original research question is
two-sample z interval for p1 − p2.
You want to design a study to estimate the proportion of students at your school who agree with the statement, "The student government is an effective organization for expressing the needs of students to the administration." You will use a 95% confidence interval, and you would like the margin of error to be 0.05 or less. The minimum sample size required is
385
Janice and her cousin Linda are a little competitive about the relative merits of their home towns. One contest they had was to determine who had more rainy days. They found weather records on the internet and each of them randomly selected 60 days from the past 5 years. Janice found that there had been measurable rainfall on 17 of the 60 days she selected for Asheville, and Linda found that there had been measurable rainfall on 12 of the 60 days she selected for Lincoln. They intend to perform a test of significance on their data, using the hypotheses H0 : pA − pL = 0 versus Ha : pA − pL ≠ 0 and the 0.05 significance level. Which of the following best describes what it would mean if Janice and Linda's test resulted in a Type I error?
Concluding that there is a difference in the proportion of rainy days in the two cities when there is no difference.
A researcher collects infant mortality data from a random sample of villages in a certain country. It is claimed that the mean death rate in this country is the same as that of a neighboring country, which is known to be 17 deaths per 1000 live births. To test this claim using a test of hypotheses, what should the null and alternative hypotheses be?
H0: mean = 17 HA: mean does not equal 17
A social psychologist reports that "in our sample, ethnocentrism was significantly higher (P < 0.05) among church attendees than among non-attendees." Which of the following statements best describes what this means?
If there were actually no difference in ethnocentrism between church attendees and non-attendees, then the chance that we would have observed a difference at least as extreme as the one we did is less than 5%.
One hundred rats with mothers that were exposed to high levels of tobacco smoke during pregnancy were put through a simple maze. At the outset, the maze required the rats to make a choice between going left and going right. Eighty of the rats went right when running the maze for the first time. Assume that the 100 rats can be considered an SRS from the population of all rats born to mothers who were exposed to high levels of tobacco smoke during pregnancy. (Note that this assumption may or may not be reasonable, but researchers often assume that lab rats are representative of large populations, since they are often bred to have uniform characteristics.) Let p be the proportion of rats in this population that would go right when running the maze for the first time. A 90% confidence interval for p is
LaTeX: 0.8\pm0.066
All of us nonsmokers can rejoice—the mosaic tobacco virus that affects and injures tobacco plants is spreading! Meanwhile, a tobacco company is investigating if a new treatment is effective in reducing the damage caused by the virus. Eleven plants were randomly chosen. On each plant, one leaf was randomly selected, and one half of the leaf (randomly chosen) was coated with the treatment, while the other half was left untouched (control). After two weeks, the amount of damage to each half of the leaf was assessed. For purposes of comparing the damage, which of the following is the appropriate type of procedure?
Matched pairs t procedures
Scientists collect data on the blood cholesterol levels (milligrams per deciliter of blood) of a random sample of 24 laboratory rats. A 95% confidence interval for the mean blood cholesterol level μ is 80.2 to 89.8. Which of the following would cause the most worry about the validity of this interval?
There is a clear outlier in the data.
A random sample of size n is collected from a Normally distributed population with standard deviation σ. Using these data, a confidence interval is computed for the mean of the population. Which of the following actions would produce a new confidence interval with a smaller width (smaller margin of error), assuming that the same data were used?
Using a lower confidence level
A 95% confidence interval for a population mean μ is calculated to be (1.7, 3.5). Assume that the conditions for performing inference are met. What conclusion can we draw for a test of H0: μ = 2 versus Ha: μ ≠ 2 at the α = 0.05 level based on the confidence interval?
We would fail to reject H0 at level α = 0.05
The student newspaper at a large university asks an SRS of 250 undergraduates,"Do you favor eliminating the carnival from the term-end celebration?" All in all, 150 of the 250 are in favor. Suppose that (unknown to you) 55% of all undergraduates favor eliminating the carnival. If you took a very large number of SRSs of size n = 250 from this population, the sampling distribution of the sample proportion would be
approximately Normal with mean 0.55 and standard deviation 0.03.
You take a sample of size 25 from a very large population in which the true proportion is p=0.1, thus violating the 10 percent condition. Which statement below best describes what you know about the sampling distribution of p with hat on top ?
mu subscript p with hat on top end subscript equals 0.1 semicolon space sigma subscript p with hat on top end subscript equals square root of fraction numerator left parenthesis 0.1 right parenthesis left parenthesis 0.9 right parenthesis over denominator 25 end fraction end root; the distribution is not approximately Normal.
The sampling distribution of a statistic is
the distribution of values taken by a statistic in all possible samples of the same sample size from the same population.
The report of a sample survey of 1,014 adults says, "With 95% confidence, between 9% and 15% of all Americans expect to spend more money on gifts this year than last year." What does the phrase "95% confidence" mean?
the method used to get the interval from 9% to 15%, when used over and over, produces intervals which include the true population percentage about 95% of the time
A researcher plans to use a random sample of families to estimate the mean monthly family income for a large population. The researcher is deciding between a 95% confidence level and a 99% confidence level. Compared to a 95% confidence interval, a 99% confidence interval will be
wider and would involve a smaller risk of being incorrect.
Most people can roll their tongues, but many can't. The ability to roll the tongue is genetically determined. Suppose we are interested in determining what proportion of students can roll their tongues. We test a simple random sample of 400 students and find that 317 can roll their tongues. The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to
0.04
Phoebe has a theory that older students at her high school are more likely to bring a bag lunch than younger students, because they have grown tired of cafeteria food. She takes a simple random sample of 80 sophomores and finds that 52 of them bring a bag lunch. A simple random sample of 104 seniors reveals that 78 of them bring a bag lunch. Letting p1= proportion of sophomores who bring a bag lunch, and p2= proportion of seniors who bring a bag lunch, Phoebe tests the hypotheses H subscript 0 colon p subscript 1 minus p subscript 2 equals 0 space a n d space H subscript a colon p subscript 1 minus p subscript 2 less than 0 at the α = 0.05 level. Phoebe's test statistic is -1.48. Which of the following is closest to the appropriate P-value for the test?
0.0694
Which of the following p-values obtained from a test of hypotheses constitutes the lease amount of evidence against the null hypothesis?
0.207
The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school.What is the probability that exactly 2 of the first 20 blood donors have Type B blood?
0.282
Janice and her cousin Linda are a little competitive about the relative merits of their home towns. One contest they had was to determine who had more rainy days. They found weather records on the internet and each of them randomly selected 60 days from the past 5 years. Janice found that there had been measurable rainfall on 17 of the 60 days she selected for Asheville, and Linda found that there had been measurable rainfall on 12 of the 60 days she selected for Lincoln. They intend to perform a test of significance on their data, using the hypotheses H0 : pA − pL = 0 versus Ha : pA − pL ≠ 0 and the 0.05 significance level. Janice and Linda's test statistic is 1.07. Which of the following is closest to the appropriate P-value for the test?
0.2846
You have an SRS of 23 observations from a large population. The distribution of sample values is roughly symmetric with no outliers. What critical value would you use to obtain a 98% confidence interval for the mean of the population?
2.508
A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election. Which of the following statements is true about the boldface numbers?
72% is a statistic and 56% is a parameter
The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school. How many blood donors should the American Red Cross expect to collect from until it gets a donor with Type B blood?
9.1 donors
A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content μ?
90% confidence; n = 50
The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: "The poll had a margin of error of plus or minus three percentage points at a 95% confidence level." You can safely conclude that
95% of all Gallup Poll samples like this one give answers within LaTeX: \pm3% of the true population value.
A letter home to the parents of seniors at Westgate High School says, "a simple random sample of 30 Westgate seniors that took the SAT-M test this year produced a mean of 512 and a standard deviation of 95. A confidence interval for the true mean for all WHS seniors is 512.00 ± 47.8." The confidence level for this interval is
99%
At a baseball game, 42 of 65 randomly selected people own an iPod. At a rock concert occurring at the same time across town, 34 of 52 randomly selected people own an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90% confidence interval for the difference in population proportions (game − concert) is (− 0.154, 0.138). Which of the following gives the correct outcome of the researcher's test of the claim?
Because the confidence interval includes 0, the researcher cannot conclude that the proportion of iPod owners at the two venues is different.
The time that it takes an untrained rat to run a standard maze has a Normal distribution with mean 65 seconds and standard deviation 15 seconds. The researchers want to use a test of hypotheses to determine whether training significantly improves the rats' completion times. An appropriate alternative hypothesis would have the form
HA: mean less than 65
Does taking garlic tablets twice a day provide significant health benefits? A researcher conducted a study of 50 adult subjects who took garlic tablets twice a day for a period of six months. At the end of the study, 100 variables related to the health of the subjects were measured for each subject, and the means were compared to known means for these variables in the population of all adults. Four of these 100 variables were significantly better (in the sense of statistical significance) at the 5% level for the group taking the garlic tablets compared to the population as a whole. One variable was significantly better at the 1% level for the group taking the garlic tablets compared to the population as a whole. Which of the following is an appropriate conclusion to draw from these results?
Neither A nor B is true.
According to a recent poll, 27% of Americans prefer to read their news in a physical newspaper instead of online. Let's assume this is the parameter value for the population. If you take a simple random sample of 25 Americans and let p with hat on top= the proportion in the sample who prefer a newspaper, is the shape of the sampling distribution of p with hat on top approximately Normal?
No, because np=6.75
In a poll, I. Some people refused to answer questions. II. People without telephones could not be in the sample. III. Some people never answered the phone in several calls. Which of these possible sources of bias is included in the ± 2% margin of error announced for the poll?
None of these
A random sample of 85 sixth-graders in a large city take a course designed to improve scores on a reading comprehension test. Based on this sample, a 90% confidence interval for the mean improvement in test scores for all sixth-graders in the city taking this course is found to be (12.6, 14.8). Which of the following are the sample mean and margin of error on which this interval is based?
Sample mean: 13.7; Margin of Error= 1.1
We would like to test the null hypothesis H0: μ = 50 against Ha: μ ≠ 50. The 95% confidence interval for μ is found to be (51.3, 54.7). Assuming all conditions for a one-sample t procedure have been met, which of the following must be true?
The P-value of the test is less than 0.05
Which of the following statements is true about Student's t distribution?
The density curve of the t distribution has heavier "tails" than the density curve of the standard Normal distribution.
An advertisement for Food Chain, a regional supermarket chain, claimed that the chain has had consistently lower prices than its regional competitors. As part of a survey conducted by an independent price-checking company, the average weekly grocery bill (based on the prices of approximately 95 commonly purchased items) was recorded for Food Chain and one of its leading competitors during 8 randomly selected weeks. We wish to conduct a test of H0: μd = 0 vs. Ha: μd < 0, where μd = the mean difference between the weekly Food Chain bill and the weekly bill at the competing chain. Which of the following is the correct Normal/Large Sample condition for conducting this test of significance?
The distribution of differences between weekly bills at the two chains should be approximately Normally distributed.
In a statistics class of 250 students, each student is instructed to toss a coin 20 times and record the value of p with hat on top , the sample proportion of heads. The instructor then makes a histogram of the 250 values of p with hat on top obtained. In a second statistics class of 200 students, each student is told to toss a coin 40 times and record the value of p with hat on top , the sample proportion of heads. The instructor then makes a histogram of the 200 values of p with hat on top obtained. Which of the following statements regarding the two histograms of p with hat on top -values is true?
The first class's histogram has greater spread (variability) because it is derived from a smaller number of tosses per student.
Suppose we conduct a test of hypotheses and find that the test results are significant at the LaTeX: \alpha=0.025 α = 0.025 level. Which of the following statements then must be true?
The results are significant at level LaTeX: \alpha=0.05
A quiz question gives random samples of n = 10 observations from each of two Normally distributed populations. Tom uses a table of t distribution critical values and 9 degrees of freedom to calculate a 95% confidence interval for the difference in the two population means. Janelle uses her calculator's two-sample t interval with 16.87 degrees of freedom to compute the 95% confidence interval. Assume that both students calculate the intervals correctly. Which of the following is true?
Tom's confidence interval is wider.
You collect test scores on four members of a population which you can safely assume is approximately Normally distributed and test the hypotheses H0 :μ =100 versus Ha :μ >100. You obtain a P-value of 0.052. Which of the following statements is true?
You have failed to obtain any evidence for Ha .
The Chipmunk population in a certain area is known to have a mean weight of 85 gm and a standard deviation of 18 gm. A wildlife biologist weighs 9 chipmunks that have been caught in live traps before releasing them. Which of the following best describes what we know about the sampling distribution of means for the biologist's sample?
mean = 85 std = 6 shape of distribution is unknown
Sweet corn of a certain variety is known to produce individual ears of corn with a mean weight of 8 ounces. A farmer is testing a new fertilizer designed to produce larger ears of corn, as measured by their weight. He finds that 32 randomly-selected ears of corn grown with this fertilizer have a mean weight of 8.23 ounces and a standard deviation of 0.8 ounces. There are no outliers in the data. Find the test statistic used to test the claim that the mean weight of the corn of the farmer is different from 8oz.
plus or minus 1.63
The distribution of prices for home sales in Minnesota is skewed to the right with a mean of $290,000 and a standard deviation of $145,000. Suppose you take a simple random sample of 100 home sales from this (very larger) population. What is the probability that the mean of the sample is above $325,000?
0.0079
The incomes in a certain large population of college teachers have a normal distribution with mean of $60,000 and standard deviation of $5000. Four teachers are selected at random from this population to serve on a salary review committee. What is the probability that their average salary exceeds $65,000?
0.0228
You are told that the proportion of those who answered "yes" to a poll about internet use is 0.70, and that the standard error is 0.0459. The sample size
is 100
The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school. What is the probability that at least 2 of the first 10 blood donors has Type B blood?
0.303
A test consists of 10 multiple choice questions with five choices for each question. As an experiment, you GUESS on each and every answer without even reading the questions. What is the probability of getting exactly 6 questions correct on this test?
0.6%
A test consists of 10 multiple choice questions with five choices for each question. As an experiment, you GUESS on each and every answer without even reading the questions. What is the probability of getting exactly 6 questions correct on this test?
0.6%
The mean of a binomial probability distribution is 857.6 and the probability of success is 64%. What is the number of values in the binomial distribution?
1340
A newspaper reporter asked an SRS of 100 residents in a large city for their opinion about the mayor's job performance. Using the results from the sample, the C% confidence interval for the proportion of all residents in the city who approve of the mayor's job performance is 0.565 to 0.695. What is the value of C?
82
A radio talk show host is interested in the proportion p of adults in his listening area who think that the drinking age should be lowered to 18. To find this proportion, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to 18?" He asks listeners to phone in and vote "yes" or "no" depending upon their opinions. Of 200 people who phone in, 140 answer "yes." The standard error of the sample proportion p with hat on top of "yes" votes among those who phone in is
0.032
Let the random variable X represent the weight of male black bears before they begin hibernation. Research has shown that X is approximately Normally distributed with a mean of 250 pounds and a standard deviation of 50 pounds. What is P(X > 325 pounds)?
0.0668
An algebra 2 test has 5 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 5 questions, what is the probability that you get at least 1 question correct?
0.7627
Resting pulse rate is an important measure of the fitness of a person's cardiovascular system, with a lower rate indicative of greater fitness. The mean pulse rate for all adult males is approximately 72 beats per minute. A random sample of 25 male students currently enrolled in the Agriculture School at a major university was selected and the mean resting pulse rate was found to be 80 beats per minute with a standard deviation of 20 beats per minute. The experimenter wishes to test if the students are less fit, on average, than the general population. Which of the following describes a Type II error in this setting? Correct Answer
Not concluding that the students are less fit (on average) as the general population when in fact they are less fit (on average).
You are testing the hypothesis that a new method for freezing green beans preserves more vitamin C in the beans than the conventional freezing method. Beans frozen by the conventional methods are known to have a mean Vitamin C level of 12 mg per serving, so you are testing H0 :μ =12 versus Ha: μ > 12, where μ = the mean amount of vitamin C (in mg per serving) in beans frozen using the new method. You calculate that the power of the test against the alternative Ha: μ = 13.5 is 0.75. Which of the following is the best interpretation of this value?
The probability of concluding that the true mean is higher than 12 mg/serving when it is actually 13.5 mg/serving.
Which one of these variables is a continuous random variable?
The time it takes a randomly selected student to complete an exam.
A researcher plans to use a random sample of families to estimate the mean monthly family income for a large population. The researcher is deciding between a sample of size n = 500 and a sample of size n= 1000. Compared to using a sample size of n = 500, a 95% confidence interval based on a sample size of n = 1000 will be
narrower and would have the same risk of being incorrect.
You are constructing a 90% confidence interval for the difference of means from simple random samples from two independent populations. The sample sizes are n1 = 6 and n2 =14. You draw dot plots of the samples to check the normality condition for two-sample t-procedures. Which of the following descriptions of those dot plots would suggest that it is safe to use t-procedures? I. The dot plot of sample 1 is roughly symmetric, while the dot plot of sample 2 is moderately skewed left. There are no outliers. II. Both dot plots are roughly symmetric. Sample 2 has an outlier. III. Both dot plots are strongly skewed to the right. There are no outliers.
t-procedures are not recommended in any of these cases.
The owner of a pet store is trying to decide whether to discontinue selling specialty clothes for pets. She suspects that only 4% of the customers buy specialty clothes for their pets. What is the probability that she does NOT sell a garment until the 7th customer? Assume each customer is independent.
0.0313
There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The standard deviation for the number of questions guessed correctly is
1.94
To determine the reliability of experts who interpret lie detector tests in criminal investigations, a random sample of 280 such cases was studied. The results were
15/280
A city school board claims that the mean number of school days missed due to illness by the city's schoolteachers is 5 per year. The teacher's union thinks it actual mean is lower than that. A random sample of 28 city school teachers missed an average of 4.5 days last year, with a sample standard deviation of 0.9 days. The distribution of the number of days missed in the sample is roughly symmetric with no outliers. A test of H0: μ = 5 and Ha: μ < 5 produces a P-value in which of the following intervals?
Between 0.0025 and 0.005
Suppose you take a sample of 50 students from your school and find the mean height of the students in your sample. Which one of the following does the sampling distribution of the mean describe?
The distribution of means of all possible samples of size 50 that could be selected from your school.
Two species of sunfish, pumpkinseeds and bluegills, are common in Puffer's Pond. For many years, the proportion of bluegills was 0.42, but a local ecologist suspects that a newly-introduced predator is increasing that proportion. He collects 50 sunfish with a net and finds that 27 of them are bluegills. Assuming that we can treat his net sample as a simple random sample, which of the following is the correct check of the Large Counts condition for a one-sample z-test of
both are greater than 10
Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary slightly from bag to bag and are Normally distributed with mean μ . A representative of a consumer advocacy group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses H0 :μ =14 Ha :μ <14 A Type I error in this situation would mean:
concluding that the bags are being underfilled when they actually aren't.
Which of the following is not a required condition for performing a t-test about an unknown population mean μ ?
The population standard deviation σ is known.
You are constructing a 90% confidence interval for the difference of means from simple random samples from two independent populations. The sample sizes are n1 = 6 and n2 =14. You draw dot plots of the samples to check the normality condition for two-sample t-procedures. Which of the following descriptions of those dot plots would suggest that it is safe to use t-procedures?
t-procedures are not recommended in any of these cases.