1. Steve listens to his favorite streaming music service when he works out. He wonders whether the service algorithm does a good job of finding random
... [Show More] songs that he will like more often than not. To test this, he listens to 50 songs chosen by the service at random and finds that he likes 32 of them.
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2. A magazine regularly tested products and gave the reviews to its customers. In one of its reviews, it tested 2 types of batteries and claimed that the batteries from company A outperformed batteries from company B in 108 of the tests. There were 200 tests. Company B decided to sue the magazine, claiming that the results were not significantly different from 50% and that the magazine was slandering its good name.
3. A candidate in an election lost by 5.8% of the vote. The candidate sued the state and said that more than 5.8% of the ballots were defective and not counted by the voting machine, so a full recount would need to be done. His opponent wanted to ask for the case to be dismissed, so she had a government official from the state randomly select 500 ballots and count how many were defective. The official found 21 defective ballots.
4. A researcher claims that the incidence of a certain type of cancer is < 5%. To test this claim, a random sample of 4000 people are checked and 170 are found to have the cancer
5. A researcher is investigating a government claim that the unemployment rate is < 5%. TO test this claim, a random sample of 1500 people is taken and it is determined that 61 people were unemployed.
6. An economist claims that the proportion of people that plan to purchase a fully electric vehicle as their next car is greater than 65%.
7. Colton makes the claim to his classmates that < 50% of newborn babies born this year in his state are boys. To prove this claim, he selects a random sample of 344 birth records in his state from this year. Colton found that 176 of the newborns were boys. What are the null and alternative hypothesis for this hypothesis test.
Answer
8. An Airline company claims that in its recent advertisement that at least 94% of passenger luggage that is lost is recovered and reunited with their customer within 1 day. Hunter is a graduate student studying statistics. For a research project, Hunter wants to find out whether there is sufficient evidence in support of the airline company’s claim. He randomly selects 315 passengers whose luggage was lost by the airlines and found out that 276 of those passengers were reunited with their luggage within 1 day. Are all of the conditions for his hypotheses test met, and if so, what are the Ho and Ha for this hypothesis test?
9. A college administrator claims that the proportion of students who are nursing majors is > 40%. To test this claim, a group of 400 students are randomly selected and its determined that 190 are nursing majors. The following is the set up for the hypothesis test: Ho: p = .40 and Ha: p = >.40
10. A hospital administrator claims that the proportion of knee surgeries that are successful are 87%. To test this claim, a random sample of 450 patients who underwent knee surgery is taken and it is determined that 371 patients had a successful knee surgery operation. Ho: p = 0.87 Ha: p ≠ 0.87 (two sided tail)
11. Jose, a competitor in cup stacking, has a sample stacking time mean of 7.5 seconds from 13 trials. Jose still claims that his average stacking time is 8.5 seconds, and the low average can be contributed to chance. At the 2% significant level, does the data provide sufficient evidence to conclude that Jose’s mean stacking time is less than 8.5 seconds? Given the sample data below, select or reject the hypothesis. (If p=value is < alpha value, we would automatically reject the hypothesis)
12. Marty, a typist, claims his average typing speed is 72 wpm. During a practice session, Marty has a sample typing speed mean of 84 wpm based on 12 trials. At the 5% significance level, does the data provide sufficient evidence to conclude that his mean typing speed is >72 wpm? Accept or reject the hypothesis given the data below.
13. What is the p-value of a two-tailed one mean hypothesis test, with a test statistic of Zo = 0.27? (Do not round your answer. Compute your answer using a value from the table. (Value in table was 0.606)
14. Raymond, a typist, claims his average typing speed is 89 wmp. During a practice session, Raymond has a sample typing speed mean of 95.5 wmp based on 15 trials. At the 1% significance level, does the data provide sufficient evidence to conclude that his mean typing speed is > 89 wmp? Accept or reject the hypothesis given the sample data below:
15. Kurtis is a statistician who claims that the average salary of an employee in the city of Yarmouth is no more than $55,000 per year. Gina, his colleague, believes this to be incorrect, so she randomly selects 61 employees who work in Yarmouth and record their annual salary. Gina calculates the sample mean income to be $56.500 per year with a sample standard deviation of $3750. Using the alternative hypothesis, Ha = μ=¿ $ 55,000 , find the test statistic τ and the p-value for the appropriate hypothesis test. Round the τ to 2 decimal places and the p-value to 3 decimal places.
16. A college administrator claims that the proportion of students that are nursing majors is less than 40%. To test this claim, a group of 400 students are randomly selected and its determined that 149 are nursing majors.
17. A researcher claims that the incidence of a certain type of cancer is less than 5%. To test this claim, the a random sample of 4000 people are checked and 170 are determined
to have the cancer.
18. A police office claims that the proportion of people wearing seat belts is less than 65%.
To test this claim, a random sample of 200 drivers is taken and its determined that 126 people are wearing seat belts.
19. A police officer claims that the proportion of accidents that occur in the daytime (versus nighttime) at a certain intersection is 35%. To test this claim, a random sample of 500 accidents at this intersection was examined from police records it is determined that 156 accidents occurred in the daytime.
20. A teacher claims that the proportion of students expected to pass an exam is greater than 80%. To test this claim, the teacher administers the test to 200 random students and determines that 151 students pass the exam.
21. A researcher claims that the proportion of smokers in a certain city is less than 20%. To test this claim, a random sample of 700 people is taken in the city and 150 people
indicate they are smokers.
22. A researcher claims that the proportion of people who are right-handed is 70%. To test this claim, a random sample of 600 people is taken and its determined that 397 people are right handed.
23. Kathryn, a golfer, has a sample driving distance mean of 187.3 yards from 13 drives. Kathryn still claims that her average driving distance is 207 yards, and the low average can be attributed to chance. At the 1% significance level, does the data provide sufficient evidence to conclude that Kathryn's mean driving distance is less than 207 yards? Given the sample data below, accept or reject the hypothesis.
24. Mary, a javelin thrower, claims that her average throw is 61 meters. During a practice session, Mary has a sample throw mean of 55.5 meters based on 12 throws. At the 1% significance level, does the data provide sufficient evidence to conclude that Mary's mean throw is less than 61 meters? Accept or reject the hypothesis given the sample data below.
25. Elizabeth claims that her average typing speed is at least 87 words per minute From recent typing trials, it is observed that Elizabeth has a sample typing speed mean
of 98.9 words per minute (based on 18 trials).
Given the sample data below, determine whether to reject the null hypothesis, or fail to reject the null hypothesis and also come to a conclusion regarding the claim.
• H0:μ=87 words per minute;
Ha:μ<87 words per minute
• α=0.01 (significance level)
• z0=1.92
• p=0.0274
26. Shawn, a competitor in cup stacking, has a sample stacking time mean of 9.2 seconds from 13 trials. Shawn still claims that her average stacking time is 8.5 seconds, and the high average can be attributed to chance. At the 4% significance level, does the data provide sufficient evidence to conclude that Shawn's mean stacking time is greater
than 8.5 seconds? Given the sample data below, accept or reject the hypothesis.
• H0:μ=8.5 seconds; Ha:μ>8.5 seconds
• α=0.04 (significance level)
• z0=0.61
• p=0.2709
27. Ruby, a bowler, has a sample game score mean of 125.8 from 25 games. Ruby still claims that her average game score is 140, and the low average can be attributed to chance. At the 5% significance level, does the data provide sufficient evidence to conclude that Ruby's mean game score is less than 140? Given the sample data below, accept or reject the hypothesis.
• H0:μ=140; Ha:μ<140
• α=0.05 (significance level)
• z0=−0.52
• p=0.3015
28. Timothy, a bowler, has a sample game score mean of 202.1 from 11 games. Timothy still claims that his average game score is 182, and the high average can be attributed to chance. At the 5% significance level, does the data provide sufficient evidence to conclude that Timothy's mean game score is greater than 182? Given the sample data below, accept or reject the hypothesis.
• H0:μ=182; Ha:μ>182
• α=0.05 (significance level)
• z0=1.57
• p=0.0582
29. What is the p-value of a two-tailed one-mean hypothesis test, with a test statistic of z0=−1.59? (Do not round your answer; compute your answer using a value from the table below.)
30. What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic of z0=2.05? (Do not round your answer; compute your answer using a value from the table below.) The number on the table was . 980
31. What is the p-value of a left-tailed one-mean hypothesis test, with a test statistic of z0=−1.19?
32. What is the p-value of a left-tailed one-mean hypothesis test, with a test statistic
of z0=−0.65? (Do not round your answer; compute your answer using a value from the table below. [Show Less]