According to a government website, 42 percent of US citizens are Democrats, 34 percent are Republicans, and 24 percent are Independents. A local municipality would like to know if the distribution of political party affiliation among its citizens differs from the nationwide percentages. A random sample of 500 citizens of the municipality is selected. Are the conditions for inference met?
A prize wheel at a carnival consists of five equal sectors of these colors: red, blue, green, yellow, and orange. If the wheel lands on yellow, the player wins a prize. After observing several spins, a customer suspects that the wheel is not fair. To substantiate this belief, the customer observes 100 consecutive spins of the prize wheel. Are the conditions for inference met?
As products come off a large assembly line, they are inspected for quality. They are placed into one of three categories: pass, fail, or need additional inspection. The manager claims that 80 percent of the products pass the inspection, 5 percent fail, and 15 percent need additional inspection. In an effort to increase the passing rate, the machines are recalibrated. After this recalibration, a random sample of 100 products is selected. The manager would like to know if there is convincing evidence that the distribution has changed. What are the appropriate hypotheses?
A prize wheel at a carnival consists of five equal sectors of these colors: red, blue, green, yellow, and orange. If the wheel lands on yellow, the player wins a prize. After observing several spins, a customer suspects that the wheel is not fair. To substantiate this belief, the customer observes 100 consecutive spins of the prize wheel. What are the appropriate hypotheses?
According to a government website, 42 percent of US citizens are Democrats, 34 percent are Republicans, and 24 percent are Independents. A local municipality would like to know if the distribution of political party affiliation among its citizens differs from the nationwide percentages. A random sample of 500 citizens of the municipality is selected. What are the appropriate hypotheses?
A manufacturer of large kitchen appliances keeps track of the costs of warranty claims. Management suspects that 75 percent of all warranty claims are invalid, 20 percent cost the company less than 500 dollars , and 5 percent of them cost the company more than 500 dollars To investigate this belief, a random sample of 80 warranty claims is selected from their vast records of past warranty claims. The management would like to know if the distribution of claim results differs from what they suspect. Are the conditions for inference met?
An employee claims that 20 percent of the email she receives is personal, 60 percent is work related, and 20 percent is spam. The high level of spam she is receiving is frustrating, so she creates some new filters. She then selects a random sample of 50 emails over the next several weeks. She would like to know if the distribution of emails she receives has changed. What are the appropriate hypotheses?
It is common knowledge that a fair coin lands heads up 50 percent of the time and tails up 50 percent of the time. For fair coins, a probability of 0 is assigned to the coin landing on its edge. But what if several coins were glued together? A teacher claims that if 10 pennies were glued together and flipped many times, the penny stack would land on heads 25 percent of the time, tails 25 percent of the time, and on its edge 50 percent of the time. To investigate this claim, a student glues 10 pennies together and flips the stack 200 times. The student would like to know if there is convincing evidence that the distribution differs from what the teacher claimed. What are the appropriate hypotheses?
Students at a large university have four places to get lunch: the cafeteria, the hut, the taco wagon, or the pizza place. An article in the school newsletter states that 70 percent of students prefer to get lunch in the cafeteria and the other three options are preferred equally. To investigate this claim, a random sample of 150 students is selected. What are the appropriate hypotheses?
Students at a large university have four places to get lunch: the cafeteria, the hut, the taco wagon, or the pizza place. An article in the school newsletter states that 70 percent of students prefer to get lunch in the cafeteria and the other three options are preferred equally. To investigate this claim, a random sample of 150 students is selected. Are the conditions for inference met?
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