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A one-sample z-test for a population proportion.
A study reports that 75 percent of young adults in a county get their news from online sources. A sociologist believes that the percentage is actually greater than 75 percent. The sociologist will select a random sample of young adults from around the county to interview. Which of the following is the most appropriate method for investigating the sociologist's belief?
A one-sample z-test for a population proportion.
A study reported that 28 percent of middle school students in a certain state participate in community service activities. A teacher believes that the rate is greater than 28 percent for the middle school students in the teacher's district. The teacher selected a random sample of middle school students from the district, and the percent of students in the sample who participated in community service activities was found to be 32 percent. Which of the following is the most appropriate method for investigating the teacher's belief?
H0:p=0.5
Ha:p>0.5
A workers' representative for a large factory believes that more than half the workers at the factory want the opportunity to work more overtime hours. Which of the following are the appropriate hypotheses to test the representative's belief?
H0: p=0.12
Ha: p<0.12
A manufacturer of cell phone screens is concerned because 12 percent of the screens manufactured using a previous process were rejected at the final inspection and could not be sold. A new process is introduced that is intended to reduce the proportion of rejected screens. After the process has been in place for several months a random sample of 100 screens is selected and inspected. Of the 100 screens 6 are rejected. What are the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected?
2 only
A one-sample z-test for a population proportion p will be conducted. Which of the following conditions checks that the sampling distribution of the sample proportion is approximately normal?
1)The sample is selected at random.
2)np0≥10 and n(1−p0)≥10 for sample size n.
3)The sample size is less than or equal to 10 percent of the population size.
The expected number of teens in the sample who do not use social media is less than 10.
A newspaper article claims that 92 percent of teens use social media. To investigate the claim, a polling organization selected a random sample of 100 teens, and 96 teens in the sample indicated that they use social media. Given the data, why is it not appropriate to use a one-sample z-test for a proportion to test the newspaper's claim?
z= (0.24-0.20)/square root (0.20)(0.80)/150
A state biologist is investigating whether the proportion of frogs in a certain area that are bullfrogs has increased in the past ten years. The proportion ten years ago was estimated to be 0.20. From a recent random sample of 150 frogs in the area, 36 are bullfrogs. The biologist will conduct a test of H0:p=0.20 versus Ha:p>0.20. Which of the following is the test statistic for the appropriate test?
0.0122
A hypothesis test was conducted to investigate whether the population proportion of students at a certain college who went to the movie theater last weekend is greater than 0.2. A random sample of 100 students at this college resulted in a test statistic of 2.25. Assuming all conditions for inference were met, which of the following is closest to the p-value of the test?
square root (0.36)(0.54)/150
In the United States, 36 percent of the people have a blood type that is A positive. From a random sample of 150 people from Norway, 66 had a blood type that was A positive. Consider a hypothesis test to investigate whether the proportion of people in Norway with a blood type of A positive is different from that in the United States. Which of the following is the standard deviation used to calculate the test statistic for the one-sample z-test?
If the population proportion is 0.80, the probability of observing a sample proportion of at least 0.84 or at most 0.76 is 0.273.
Molly works for a meat producer, and she needs to determine whether containers of ground beef have the correct fat content. She obtains a random sample of 120 containers of ground beef and finds that 84 percent have the correct fat content. Molly then conducts a hypothesis test of H0:p=0.80 versus Ha:p≠0.80 and calculates a test statistic of 1.10 with a p-value of 0.273. Which of the following best represents the meaning of the p-value?If the population proportion is 0.80, the probability of observing a sample proportion of at least 0.84 or at most 0.76 is 0.273.
Of all possible samples of the same size, 3.22% will result in a success rate of 93.6% or less.
Chicken hatcheries employ workers to determine the sex of the baby chicks. The hatcheries claim that the workers are correct 95 percent of the time. An investigator believes the workers' success rate (workers are correct) is actually less than 95 percent of the time. The investigator selects a random sample of chicks and finds that the hatchery workers had a success rate of 0.936. The conditions for inference were checked and verified, and the p-value of the test was given as 0.0322. If the null hypothesis is true, which of the following statements is a correct interpretation of the p-value?
The null hypothesis is true.
In a hypothesis test for a single proportion, which of the following is assumed for the calculation of the p-value?
No, because the p-value 0.053 is greater than the significance level 0.05.
A major credit card company is interested in the proportion of individuals who use a competitor's credit card. Their null hypothesis is H0: p=0.65, and based on a sample they find a sample proportion of 0.70 and a p-value of 0.053. Is there convincing statistical evidence at the 0.05 level of significance that the true proportion of individuals who use the competitor's card is actually greater than 0.65 ?
At the significance level α=0.05, the null hypothesis is rejected. There is convincing evidence to support the claim that fewer than 40% of the students at the local university read at least one book last year.
A book club wonders if fewer than 40 percent of students at a local university had read at least one book during the last year. To test the claim, the book club selected a random sample of students at the local university and recorded the number of students who had read at least one book during the last year. The club conducted a test with the hypotheses H0:p=0.40 versus Ha:p<0.40. The test yielded a p-value of 0.033. Assuming all conditions for inference were met, which of the following is an appropriate conclusion?
No, the significance level is the probability of rejecting the null hypothesis when the null hypothesis is actually true.
Is the significance level of a hypothesis test equivalent to the probability that the null hypothesis is true?
Origin of the Federalist Political Party (1790’s)
During debates over ratification of the new U.S. Constitution in 1788, divisions emerged among political leaders in the 1790s. On one side, a leading Secretary of the Treasury advocated for a strong federal government with a loose interpretation of the Constitution—supporting powers deemed “necessary and proper” for Congress. His followers, largely large landowners, bankers, and businessmen in New England and the middle states, also favored closer ties with England in foreign affairs. The last president from this faction eventually saw the party fade after 1800.
Origin of the Democratic-Republican Party (1790’s)
Amid debates over the scope of federal power during the Constitution’s ratification, a prominent Secretary of State and a key ally from Virginia championed a vision of limited government. Favoring a strict interpretation of the Constitution, they argued that Congress and the President should exercise only those powers explicitly granted. With support from another influential Virginian, they promoted policies favoring agriculture in the South and closer alignment with France, setting the stage for a political coalition that eventually became known by this name.
Election of 1800
In a landmark and bloodless transfer of power, a sitting president from one party ran for a second term but was defeated by a rival candidate representing a different faction. The contest became so deadlocked that the House of Representatives had to decide the outcome after his Vice-Presidential candidate tied with his opponent. Influential support from a leading Cabinet member—who distrusted the rival’s running mate—helped break the tie, marking the first time control of the government shifted from one party to another without violence.
Midnight Appointments (1801)
In the final hours of his presidency, after an electoral defeat, a departing president hurried to secure his party’s legacy by appointing a large number of Federalist judges and officials to federal positions—positions that included key roles in the judiciary and local governance. Some appointment papers were delayed or undelivered when the new administration took over, prompting its Secretary of State to block their delivery. This dispute later escalated into a landmark Supreme Court case that established the principle of judicial review.
Louisiana Purchase (1803)
In 1803, under the leadership of a president known for his belief in limited government and expansion, the United States doubled its size by purchasing over 800,000 square miles from Napoleon’s France for $15 million. This vast territory, stretching from the Mississippi River to the Rocky Mountains, prompted an expedition led by renowned explorers to map and study the new lands, laying the groundwork for future westward expansion.
