Stat Test Practice Test 4
Suppose that a study of 1000 female teenagers in Atlanta found that 233 of them gave birth in 2016. Given that the population proportion is understood to be p=0.237, what would be the alternative hypothesis, Ha, for this study?
Ha: p < 23.7%
The histogram below is from a simulation of the difference between two population proportions. The mean and the standard error are calculated using the population proportion values and the sample size values. Which of the following is the best estimate of the population proportions?
The population proportions are 0.70 and 0.55.
Quit Smoking:The New England Journal of Medicine published the results of a double-blind, placebo-controlled experiment to study the effect of nicotine patches study the effect of nicotine patches versus a placebo on quitting smoking. With the data from the experiment we calculate the sample difference in the "quit smoking" rates for the nicotine treatment group and the placebo group ("treatment" minus "placebo"). We get 0.8%=0.008. The 99% confidence interval based on this sample difference is -0.1036 to 0.0882. We also calculate a 90% confidence interval. How does the 90% confidence interval compare to the 99% confidence interval? For a 90% confidence interval, the margin of error (MOE) will:
Decrease
In the article "Coffee, Caffeine, and Risk of Depression Among Women" in the September 2011 edition of the Archives of Internal Medicine, researchers investigated the relationship between caffeine consumption and depression among women. The participants in this study were older, with substantially lower rates of depression when compared to female teens. Researchers compared two groups of women (among others) in this study: those who do not drink coffee and those who routinely drink 4 or more cups of coffee each day. For the following question, a coffee drinker is a woman who drinks four or more cups each day. One of the graphs below represents the sampling distribution of differences between the sample proportions for depressed coffee and non-coffee drinking women. Under the assumption that both women who drink coffee and do not drink coffee have a 6% depression rate, which distribution of differences in sample proportions is centered correctly?
Graph A- last number is .04
Short-term classes: Does taking a class in a short-term format (8 weeks instead of 16 weeks) increase a student's likelihood of passing the course? For a particular course, the pass rate for the 16-week format is 59%. A team of faculty examine student data from 40 randomly selected accelerated classes and determine that the pass rate is 78%. Which of the following are the appropriate null and alternative hypotheses for this research question?
H0: p = 0.59; Ha: p > 0.59
A politician claims that a larger proportion of members of the news media are Democrats when compared to the general public. Let p1 represent the proportion of the news media that is Democrat and p2 represent the proportion of the public that is Democrat. What are the appropriate null and alternative hypotheses that correspond to this claim?
H0: p1 - p2 = 0; Ha: p1 - p2 > 0
A researcher conducts an experiment on human memory and recruits 15 people to participate in her study. She performs the experiment and analyzes the results. She uses a t-test for a mean and obtains a p-value of 0.17. Which of the following is a reasonable interpretation of her results?
If there is a treatment effect, the sample size was too small to detect it.
Genetically modified foods: According to a 2016 Pew Research survey, a majority of the American general public (57%) says that genetically modified (GM) foods are generally unsafe to eat. This month, in a survey of 500 randomly selected American adults, 60% says that GM foods are generally unsafe to eat. We test the hypothesis that the percentage who says that GM foods are generally unsafe to eat is greater than 57% this year. The p-value is 0.085. Which of the following interpretations of this p-value is valid?
If we assume that 57% of Americans says that GM foods are generally unsafe to eat, then there is an 8.5% chance that random sample results will show 60% or more who says that GM foods are generally unsafe to eat.
Quit Smoking: The New England Journal of Medicine published the results of a double-blind, placebo-controlled experiment to study the effect of nicotine patches and the antidepressant bupropion on quitting smoking. With the data from the experiment we calculate the sample difference in the "quit smoking" rates for the nicotine treatment group and the placebo group ("treatment" minus "placebo"). We get 0.8% = 0.008. Which of the following is an appropriate conclusion based on this finding?
In this experiment the nicotine treatment had a higher success rate than the placebo group, but the improvement was less than 1%.
In March 2015, the Public Policy Institute of California (PPIC) surveyed 7,525 likely voters living in California. In the survey, respondents were asked about global warming. PPIC researchers are interested in the difference in viewpoints across racial/ethnic groups. PPIC results show that 75% of Latinos view global warming as a serious problem, and 46% of whites view global warming as a serious problem. Using the data from the survey, we calculate the sample difference in global warming viewpoints for Latino respondents and white respondents to be 29% = 0.29. Researchers can use the 29% sample difference to draw a conclusion about which populations?
Latinos and whites living in California who are likely to vote
In a study at West Virginia University Hospital, researchers investigated smoking behavior of cancer patients to create a program to help patients stop smoking. They published the results in Smoking Behaviors Among Cancer Survivors (January 2009 issue of the Journal of Oncology Practice.) In this study, the researchers sent a 22-item survey to 1,000 cancer patients. They collected demographic information (age, sex, ethnicity, zip code, level of education), clinical and smoking history, and information about quitting smoking. The questionnaire filled out by cancer patients at West Virginia University Hospital also asked patients if they were current smokers. The current smoker rate for female cancer patients was 11.6%. 95 female respondents were included in the analysis. For male cancer patients, the current smoker rate was 10.4%, and 67 male respondents were included in the analysis. Suppose that these current smoker rates are the true parameters for all cancer patients. Can we use a normal model for the sampling distribution of differences in proportions?
No, a normal model is not a good fit for this sampling distribution.
In 2014, students in an advanced Statistics course at UC Berkeley conducted an anonymous survey about use of cognition-enhancing drugs among college males. One survey group of males included members from a fraternity, and the other survey of males group included no fraternity members. The difference between the proportion of fraternity members who have used cognition-enhancing drugs and the proportion of non-fraternity members who have used cognition-enhancing drugs is equal to 0.054. Which one of the following conclusions is true?
One possibility is that the proportion of fraternity members who have used cognition-enhancing drugs is 0.295 and the proportion of non-fraternity members who have used cognition-enhancing drugs is 0.241.
Every simulation in this module is based on an assumption about the difference between two population proportions. The population proportions affect the mean and the standard error of the differences in sample proportions. The sample size also affects the standard error. The distribution of differences between sample proportions shown below has mean 0.35, and a standard error of about 0.10. Which of the following did we use to generate this sampling distribution?
Population proportions of 0.85 and 0.50 with samples of size 35.
We conduct a study to determine whether the majority of community college students plan to vote in the next presidential election. We choose a significance level of 0.05. We survey 650 randomly selected community college students and find that 54% of them plan to vote. The p-value is 0.02. H0: 50% of community college students plan to vote in the next presidential election. Ha: More than 50% of community college students plan to vote in the next presidential election. What can we conclude?
The evidence suggests that the majority of community colleges students plan to vote in the next presidential election because the p-value is less than the significance level.
Living with parents: A Pew Research analysis stated that in 2012, 36.6% of the nation's young adults ages 18-31—the so-called Millennial generation—were living in their parents' home. After reading the analysis, a statistics student wanted to design a study to determine if the percentage was higher for the Millennial students who attend his college. Which of the following is an appropriate statement of the null hypothesis?
The percentage of Millennial students at his college who live in their parents' home is the same as the percentage of Millennials nationwide, i.e., H0: p = 36.6% Correct. We assume that the percentage of Millennial students at his college who live in their parents' home is the same as the percentage of Millennials nationwide. Thus H0 states that the percentage is 36.6%.
Watches and bacteria: A group of researchers investigated the contamination of medical personnel watches at a New York hospital, since there is a potential for patient exposure to potentially dangerous bacteria. They sampled watches worn by physicians, physician assistants, and medical students at a teaching hospital in New York. Nearly half (46.6%) of the watches tested harbored microorganisms that can cause illness. By comparison, only one of the 10 watches worn by security guards tested positive for a disease-carrying microorganism. The researchers want to determine if the difference is statistically significant. Which of the following is an appropriate statement of the null hypothesis, H0?
The proportion of contaminated wrist-watches from medical personnel is the same as the proportion of contaminated wrist-watches from security guards, i.e., H0: p = 46.6%.
The histogram below is from a simulation of the difference between two population proportions. The mean and the standard error are calculated using the population proportion values and the sample size values. Which of the following is the best estimate of the standard error?
The standard error is 0.05.
Pregnancy testing: A college student hasn't been feeling well and visits her campus health center. Based on her symptoms, the doctor suspects that she is pregnant and orders a pregnancy test. The results of this test could be considered a hypothesis test with the following hypotheses: H0: The student is not pregnant Ha: The student is pregnant. Based on the hypotheses above, which of the following statements is considered aType I error?
The student is not pregnant, but the test result shows she is pregnant.
Pregnancy testing: A college student hasn't been feeling well and visits her campus health center. Based on her symptoms, the doctor suspects that she is pregnant and orders a pregnancy test. The results of this test could be considered a hypothesis test with the following hypotheses: H0: The student is not pregnant Ha: The student is pregnant. Based on the hypotheses above, which of the following statements is considered a Type II error?
The student is pregnant, but the test result shows she is not pregnant.
A 2014 study by the reputable Gallup organization estimates that 44% of U.S. adults are underemployed. Underemployed means the person wants to work full time but is employed part time or unemployed. We want to know if the proportion is smaller this year. We select a random sample of 100 U.S. adults this year and find that 40% are underemployed. After carrying out the hypothesis test for p = 0.44 compared to p < 0.44, we obtain a P‑value of 0.21. Which of the following interpretations of the P‑value is correct?
There is a 21% chance that a sample of 100 U.S. adults will have 40% or fewer underemployed if 44% of the population is underemployed this year.
In 2014, students in an advanced Statistics course at UC Berkeley conducted an anonymous survey about use of cognition-enhancing drugs among college males. One survey group of males included members from a fraternity, and the other survey of males group included no fraternity members. We can use a simulation model to estimate the true difference between the proportion of fraternity members who have used cognition-enhancing drugs and the proportion of non-fraternity members who have used cognition-enhancing drugs. The graph below represents the sampling distribution of differences. The difference in proportions is p1 - p2 = 0.05 (fraternity members minus non-fraternity members), and the standard error is 0.08. The z-score for this difference in sample proportions is 0.885. Which of the following is the most appropriate conclusion?
There is not a statistically significant difference between the proportion of fraternity members who have used cognition-enhancing drugs and the proportion of non-fraternity members who have used cognition-enhancing drugs.
In March 2015, the Public Policy Institute of California (PPIC) surveyed 7525 likely voters living in California. This is the 148th PPIC research poll, and is part of a survey series that started in 1998. PPIC researchers find that 3266 survey participants are registered Democrats and 2137 survey participants are registered Republicans. PPIC is interested in the difference in approval rate for the governor between registered Democrats and registered Republicans in California. Participants were asked: "Overall, do you approve or disapprove of the way the governor of California is handling his job?" 2450 of the registered Democrats answered "Yes" and 684 of the registered Republicans answered "Yes." True or false? A normal model is an appropriate fit for the sampling distribution of sample differences.
True Correct. The counts of successes (answered "Yes") and failures (answered "No") must be at least 10 for a normal model to be a good fit. Both Democrats and Republicans have large sample sizes, with n1=3266 and n2=2137 people. The calculations n1p1, n1(1-p1), n2p2, and n2(1-p2) are all greater than 10.
Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses. H0: The food is safe. Ha: The food is not safe. Based on the hypotheses above, is the following statement a Type I or Type II error? The sample suggests that the food is not safe, but it actually is safe
Type I
Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses. H0: The food is safe. Ha: The food is not safe Based on the hypotheses above, Is the following statement a Type I or Type II error? The sample suggests that the food is safe, but it actually is not safe.
Type II
The 99% confidence interval for the difference in proportions of women and men who support stricter gun control is (0.02, 0.08). (Difference here is "women" minus "men.") Which of the following conclusions about the confidence interval is most appropriate?
We are 99% confident that the difference between the proportions of women and men who support stricter gun control is between 0.02 and 0.08.
Facebook friends: According to Facebook's self-reported statistics, the average Facebook user has 130 Facebook friends. For a statistics project a student at Contra Costa College (CCC) tests the hypothesis that CCC students will average more than 130 Facebook friends. She randomly selects 3 classes from the schedule of classes and distributes a survey in these classes. Her sample contains 45 students. From her survey data she calculates that the mean number of Facebook friends for her sample is: ¯x= 138.7 with a standard deviation of: s=79.3. She chooses a 5% level of significance. What can she conclude from her data?
We cannot conclude that the average number of Facebook friends for CCC students is greater than 130. The sample mean of 138.7 is not significantly greater than 130.
According to the National Institute on Drug Abuse, a U.S. government agency, 17.3% of 8th graders in 2010 had used marijuana at some point in their lives. A school official hopes to show the percentage is lower in his district, testing H0: p = 0.173 versus Ha: p < 0.173. The health department for the district uses anonymous random sampling and finds that 10% of 80 eighth graders surveyed had used marijuana. Is the sample size condition for conducting a hypothesis test for a population proportion satisfied?
Yes, because (80)(.173) and (80)(1 ‑ 0.173) are both at least 10. This means we can use the normal distribution to model the distribution of sample proportions.
Researchers conducted a randomized, double-blind clinical trial to compare the herb St. John's Wort, the antidepressant drug sertraline, and a placebo for the treatment of depression. Of the 113 patients in the herb treatment group, 23.9% showed improvement, compared to 24.8% of the 113 in the sertraline group and 31.9% of the 113 patients in the placebo group. Medscape Medical News published this research in 2002. Is a normal model a good fit for the sampling distribution?
Yes, there are at least 10 people who improved and 10 who did not improve in each randomized treatment group.
In 2010 polls indicated that 75% of Americans favored mandatory testing of students in public schools as a way to rate the school. This year in a poll of 1,000 Americans 72% favor mandatory testing for this purpose. Has public opinion changed since 2010? We test the hypothesis that the percentage supporting mandatory testing is less than 75% this year. The p-value is 0.013. Which of the following interpretation of this p-value is valid?
.If 75% of Americans still favor mandatory testing this year, then there is a 1.4% chance that poll results will show 72% or fewer with this opinion.
One population proportion test: Which of the following situations involves testing a claim about a single population proportion?
A recent report estimated that 25% of all college students in the United States have a sexually transmitted disease (STD). The director of the campus health center believes that the proportion of students with STDs is higher at their campus.
The difference between teenage female and male depression rates estimated from two samples is 0.08. The estimated standard error of the sampling distribution is 0.04. What is the 95% confidence interval? Use the critical value z = 1.96. (, ) Round all calculations to two decimal places. Put lower bound in the first box and upper bound in the second box.
0.00,.16
In 2014, students in an advanced Statistics course at UC Berkeley conducted an anonymous survey about use of cognition-enhancing drugs among college males. One survey group of males included members from a fraternity, and the other survey of males group included no fraternity members. The graph below represents the sampling distribution of differences between the proportion of fraternity members who have used cognition-enhancing drugs and the proportion of non-fraternity members who have used cognition-enhancing drugs. The difference in proportions is p1−p2=0.05 (fraternity members minus non-fraternity members). Consider simulating this data with 5000 samples from each of the fraternity member group and the non-fraternity member group. Based on the sampling distribution of difference in proportions, which of the following results for p1−p2 would be most unusual?
0.29
In the article Foods, Fortificants, and Supplements: Where Do Americans Get Their Nutrients? researchers analyze the nutrient and vitamin intake from a random sample of 16,110 U.S. residents. Researchers compare the level of daily vitamin intake for vitamin A, vitamin B-6, vitamin B-12, vitamin C, vitamin D, vitamin E and calcium. Unless otherwise stated, all hypothesis tests in the study are conducted at the 5% significance level. For the claim that the proportion of U.S. residents who consumed recommended levels of vitamin A is higher among women than men, the null and alternative hypotheses are: The p-value is 0.08, and researchers conduct this test at a 5% level of significance. Which of the following is the correct conclusion?
Fail to Reject H0 , do not support Ha .
Students in a discussion of gun control in a sociology class at Foothill Community College argue that Republicans are more likely to oppose gun control than Independents. They use data from an article titled "Gun Control Splits America," published March 23, 2010 in pewresarch.org by the Pew Research Center for the People and the Press. In this study 62% of Republicans and 57% of Independents say that states should not be able to pass laws banning handguns. For a claim that a larger proportion of Republicans oppose state laws banning handguns when compared to Independents, the null and alternative hypotheses are The p-value is 0.06. If we conduct this test at a 5% level of significance, what would be an appropriate conclusion?
Fail to Reject H0 , do not support Ha .
A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000 miles. The manufacturer tests 250 tires that have been used for 60,000 miles. They find that 9 of them are worn out. With this data, we test the following hypotheses at the 5% significance level. The p-value is 0.15. H0: The proportion of tires that are worn out after 60,000 miles is equal to 0.05. Ha: The proportion of tires that are worn out after 60,000 miles is less than 0.05. Which of the following conclusions is correct?
Fail to reject H0
In the article Foods, Fortificants, and Supplements: Where Do Americans Get Their Nutrients? researchers analyze the nutrient and vitamin intake from a random sample of 16,110 U.S. residents. Researchers compare the level of daily vitamin intake for vitamin A, vitamin B-6, vitamin B-12, vitamin C, vitamin D, vitamin E and calcium. Unless otherwise stated, all hypothesis tests in the study are conducted at the 5% significance level. To test the claim (at 5% significance) that the proportion of U.S. residents who consume recommended levels of vitamin A is higher among women than men, researchers set up the following hypotheses: In this hypothesis test which of the following errors is a Type I error?
Researchers conclude that a larger proportion of women consume the recommended daily intake of vitamin A when there is actually no difference between vitamin A consumption for women and men.
In the article "Attitudes About Marijuana and Political Views" (Psychological Reports, 1973), researchers reported on the use of cannabis by liberals and conservatives during the 1970s. To test the claim (at 1% significance) that the proportion of voters who smoked cannabis frequently was lower among conservatives, the hypotheses were In this hypothesis test which of the following errors is a Type II error?
We conclude that there is no difference between the proportions of conservatives and liberals that smoke cannabis, when the proportion is actually lower for conservatives.
Living with parents: The Pew Research Center reported that 36% of American Millennials (adults ages 18-31) still live at home with their parents. A group of students wants to conduct a study to determine whether this result is true for students at their campus. They survey 300 randomly selected students at their campus and determine that 43% of them still live at home with their parents. With this data, they test the following hypotheses at the 5% significance level. The p-value is 0.006. H0: Of Millennial students at their campus, 36% live at home with their parents. Ha: More than 36% of Millennial students at their campus live at home with their parents. Which of the following conclusions is correct?
Reject H0
Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester. In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 41 expectant mothers have mean weight increase of 15.4 pounds in the second trimester, with a standard deviation of 5.8 pounds. A hypothesis test is done to see if there is evidence that weight increase in the second trimester is greater than 14 pounds. Find the p-value for the hypothesis test
.0650
Gardeners on the west coast of the United States are investigating the difference in survival rates of two flowering plants in drought climates. Plant A has a survival rate of 0.6 and plant B has a survival rate of 0.43. The standard error of the difference in proportions is 0.084. What is the margin of error for a 99% confidence interval? Use critical value z = 2.576. MOE =
.216
Living with parents: A Pew Research analysis stated that in 2012, 36% of the nation's young adults ages 18 to 31—the so-called Millennial generation—were living in their parents' home. After reading the analysis, a statistics student wanted to design a study to determine if the percentage was higher for the Millennial students who attended his college. Before collecting data, he set the significance level for his test to be 0.05. For which p-value would he reject the null hypothesis?
0.02
Skittles: The popular Skittles candy comes in 5 colors. According to the Skittles website, the colors are evenly distributed in the population of Skittle candies. So each color makes up 20% of the population. Suppose that we buy 2 small bags of Skittles. We determine the percentage of green Skittles in one bag and the percentage of orange Skittles in the other bag. Suppose that each bag contains 40 candies. We define the difference in sample proportions as "green" minus "orange." Which of the following will give a sample difference of 0.10?
10 green and 6 orange
Does secondhand smoke increase the risk of a low weight birth? A baby is "low birth weight" if it weighs less than 5.5 pounds at birth. According to the National Center of Health Statistics, about 7.8% of all babies born in the U.S. are categorized as low birth weight. Researchers randomly select 1200 babies whose mothers had extensive exposure to secondhand smoke during pregnancy. 10.4% of the sample are categorized as low birth weight. Which of the following are the appropriate null and alternative hypotheses for this research question
H0: p = 0.078; Ha: p > 0.078 MAYBE
In a fictional study, suppose that a psychologist is studying the effect of daily meditation on resting heart rate. The psychologist believes the patients who not meditate have a higher resting heart rate. For a random sample of 45 pairs of identical twins, the psychologist randomly assigns one twin to one of two treatments. One twin in each pair meditates daily for one week, while the other twin does not meditate. At the end of the week, the psychologist measures the resting heart rate of each twin. Assume the mean resting heart rate is 80 heart beats per minute. The psychologist conducts a T-test for the mean of the differences in resting heart rate of patients who do not meditate minus resting heart rate of patients who do meditate. Which of the following is the correct null and alternative hypothesis for the psychologist's study?
H0: µ = 0; Ha: µ > 0
A scientist claims that a smaller proportion of members of the National Academy of Sciences are women when compared to the proportion of women nationwide. Let p1 represent the proportion of women in the National Academy of Sciences and p2 represent the proportion of women nationwide. Which is the correct alternative hypotheses that corresponds to this claim?
Ha: p1 - p2 < 0
A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000 miles. The manufacturer tests 250 tires that have been used for 60,000 miles. They find that 3.6% of them are worn out. With this data, we test the following hypotheses. H0: The proportion of tires that are worn out after 60,000 miles is equal to 0.05. Ha: The proportion of tires that are worn out after 60,000 miles is less than 0.05. In order to assess the evidence, which question best describes what we need to determine?
NEED ANSWER Incorrect. In a hypothesis test we are trying to estimate the chance that random sampling produces sample results are as or more extreme than the result observed in the data if the null hypothesis is true. The statement you chose asks, in essence, "What is the chance that the population proportion is less than the null value?" In other words, the statement you chose asks, "What is the chance that the alternative hypothesis is true?" But a hypothesis test cannot determine this.
A teacher is experimenting with computer-based instruction. In which situation could the teacher use a hypothesis test for a population mean?
She gives each student a pretest. Then she teaches a lesson using a computer program. Afterwards, she gives each student a posttest. The teacher wants to see if the difference in scores will show an improvement.
Students in a discussion of gun control in a sociology class at Foothill Community College argue that Republicans are more likely to oppose gun control than Independents. They use data from an article titled "Gun Control Splits America," published March 23, 2010 in pewresarch.org by the Pew Research Center for the People and the Press. In this study 62% of Republicans and 57% of Independents say that states should not be able to pass laws banning handguns. The article states that researchers collected data from 1,500 adults nationwide reached on landlines and cell phones. Which issue will invalidate the conclusion of the hypothesis test?
The data is not a random sample. maybe??
In the article, Attitudes About Marijuana and Political Views (Psychological Reports, 1973), researchers reported on the use of cannabis by liberals and conservatives during the 1970's. To test the claim (at 1% significance) that the proportion of voters who smoked cannabis frequently was lower among conservatives, the hypotheses were In the hypothesis test about cannabis use by conservatives and liberals, the test statistic was z = -4.27, with a corresponding p-value of about 0.00001. Which conclusion is most appropriate in the context of this situation?
The data support the claim that a lower proportion of conservatives smoke cannabis when compared to liberals. maybe??
Living with parents: The Pew Research Center reported that 36% of American Millennials (adults ages 18-31) still live at home with their parents. A group of students wants to conduct a study to determine whether this result is true for students at their campus. They survey 300 randomly selected students at their campus and determine that 43% of them still live at home with their parents. With this data, they test the following hypotheses at the 5% significance level. The p-value is 0.006. H0: Of Millennial students at their campus, 36% live at home with their parents. Ha: More than 36% of Millennial students at their campus live at home with their parents. What can we conclude?
The evidence suggests that more than 36% of students at their campus live at home with their parents because the p-value is less than the significance level.
The Food and Drug Administration (FDA) is a U.S. government agency that regulates (you guessed it) food and drugs for consumer safety. One thing the FDA regulates is the allowable insect parts in various foods. You may be surprised to know that much of the processed food we eat contains insect parts. An example is flour. When wheat is ground into flour, insects that were in the wheat are ground up as well. The mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. If the FDA finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption. The null hypothesis is that the mean number of insect parts per 100 grams is 75. The alternative hypothesis is that the mean number of insect parts per 100 grams is greater than 75. Is the following a Type I error or a Type II error or neither? The test fails to show that the mean number of insect parts is greater than 75 per 100 grams when it is.
Type II error
In March 2015, the Public Policy Institute of California (PPIC) surveyed 7525 likely voters living in California. In the survey, respondents were asked about global warming. PPIC researchers are interested in the difference in viewpoints across racial/ethnic groups. PPIC results show that 75% of Latinos view global warming as a serious problem, and 46% of whites view global warming as a serious problem. Using the data from the survey, we calculate the sample difference in global warming viewpoints for Latino respondents and white respondents to be 29% = 0.29. The 95% confidence interval based on this sample difference is (0.275, 0.305). Which of the following is a valid conclusion? Check all that apply.
We are 95% confident that the true difference in proportion of Latinos who view global warming as a serious problem and whites who view global warming as a serious problem is 27.5% to 30.5%. We are 95% confident that the difference between Latino and white opinions about the severity of global warming is 29% with a margin of error of 1.5%.
College students and STDs: A recent report estimated that 25% of all college students in the United States have a sexually transmitted disease (STD). Due to the demographics of the community, the director of the campus health center believes that the proportion of students who have a STD is lower at his college. He tests H0: p = 0.25 versus Ha: p < 0.25. The campus health center staff select a random sample of 50 students and determine that 18% have been diagnosed with a STD. Is the sample size condition for conducting a hypothesis test for a population proportion satisfied?
Yes, because (50)(.25) and (50)(1 ‑ 0.25) are both at least 10. This means we can use the normal distribution to model the distribution of sample proportions.
A quality control engineer at a potato chip company tests the bag filling machine by weighing bags of potato chips. Not every bag contains exactly the same weight. But if more than 15% of bags are over-filled then they stop production to fix the machine. They define over-filled to be more than 1 ounce above the weight on the package. The engineer weighs 100 bags and finds that 21 of them are over-filled. He plans to test the hypotheses H0:p=0.15 versus Ha:p>0.15. What is the test statistic?
z = 1.68 (multiple choice)
A quality control engineer at a potato chip company tests the bag filling machine by weighing bags of potato chips. Not every bag contains exactly the same weight. But if more than 15% of bags are over-filled then they stop production to fix the machine. They define over-filled to be more than 1 ounce above the weight on the package. The engineer weighs 102 bags and finds that 32 of them are over-filled. He plans to test the hypotheses H0: p = 0.15 versus Ha: p > 0.15. What is the test statistic?
z=
In the article "Attitudes About Marijuana and Political Views" (Psychological Reports, 1973), researchers reported on the use of cannabis by liberals and conservatives during the 1970s. To test the claim (at 1% significance) that the proportion of voters who smoked cannabis frequently was lower among conservatives, the hypotheses were Suppose that we conduct a hypothesis test in which a Type II error is very serious. But the Type I error is not very serious. Which level of significance is the best choice?
α = 0.05
