## MATH 225N Week 7 Hypothesis Testing: Questions-Answers

**Question:**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 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.**Question:**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.**Question:**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.**Question:**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 … and 170 are found to have the cancer.**Question:**A researcher is investigating a government claim that the unemployment rate is < 5%. TO test this claim, a random sample of 1500 people is … and it is determined that 61 people were unemployed.**Question:**An economist claims that the proportion of people that plan to purchase a fully electric vehicle as their next car is greater than 65%.**Question:**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.**Question:**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?**Question:**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**Question:**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 (two sided tail)**Question:**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)**Question:**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.**Question:**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)**Question:**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:**Question:**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 = , find the test statistic and the p-value for the appropriate hypothesis test. Round the to 2 decimal places and the p-value to 3 decimal places.**Question:**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.**Question:**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 4000people are checked and 170 are determined to have the cancer.**Question:**A police office claims that the proportion of people wearing seat belts is less than 65%. To test this claim, a random sample of 200drivers is taken and its determined that 126 people are wearing seat belts.**Question:**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.**Question:**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 200random students and determines that 151 students pass the exam.**Question:**A researcher claims that the proportion of smokers in a certain city is less than 20%. To test this claim, a random sample of 700people is taken in the city and 150 people indicate they are smokers.**Question:**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.**Question:**Kathryn, a golfer, has a sample driving distance mean of 3yards from 13 drives. Kathryn still claims that her average driving distance is 207 yards, and the low average can … 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.**Question:**Mary, a javelin thrower, claims that her average throw is 61 During a practice session, Mary has a sample throw mean of 55.5meters 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.**Question:**Elizabeth claims that her average typing speed is at least 87words 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.**Question:**Shawn, a competitor in cup stacking, has a sample stacking time mean of 2seconds 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.**Question:**Ruby, a bowler, has a sample game score mean of 8from 25 games. Ruby still claims that her average game score is 140, and the low average can … 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.**Question:**Timothy, a bowler, has a sample game score mean of 1from 11 games. Timothy still claims that his average game score is 182, and the high average can … 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.**Question:**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.)**Question:**What is the p-value of a left-tailed one-mean hypothesis test, with a test statistic of z0=−1.19?**Question:**What is the p-value of a left-tailed one-mean hypothesis test, with a test statistic of z0=−65? (Do not round your answer; compute your answer using a value from the table below.**Question:**What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic of z0=36? (Do not round your answer; compute your answer using a value from the table below.)**Question:**What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic of z0=82? (Do not round your answer; compute your answer using a value from the table below.) Number in table was 0.966. So 1-.966 = 0.034**Question:**What is the p-value of a two-tailed one-mean hypothesis test, with a test statistic of z0=−73? (Do not round your answer; compute your answer using a value from the table below.) Table # was 0.042 so 0.042 * 2 = 0.084**Question:**A CEO wondered if her company received either more or less complaints from its workers on Monday than any other day. She figured that if it were truly random, 20%of the complaints should have been … on Monday. She randomly selected 50 complaints and checked the day that they were …. In those complaints 13 were submitted on a Monday.**Question:**The CEO conducts a one-proportion hypothesis test at the 5%significance level, to test whether the true proportion of complaints … on a Monday is different from 20%……. Which answer choice shows the correct null and alternative hypotheses for this test?**Question:**A CEO wondered if her company received either more or less complaints from its workers on Monday than any other day. She figured that if it were truly random, 20%of the complaints … on Monday. She randomly … 50complaints and … the day that they were …. In those complaints 13 were …. The CEO conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of complaints … on a Monday is different from 20%.**Question:**A business owner claims that the proportion of take out orders is greater than 25%. To test this claim, the owner checks the next 250orders and determines that 60 orders are take out orders…… The following is the setup for this hypothesis test:….. {H0:p=0.25Ha:p>0.25 …….Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.**Question:**Colton makes the claim to his classmates that less than 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 are boys. What are the null and alternative hypotheses for this hypothesis test?**Question:**Kylie works for a large nursery and is investigating whether to use a new brand of seeds. The new brand of seeds advertises that 93%of the seeds germinate, which is higher than the germination rate of the seeds she is currently using. She will change over to this new brand unless the actual germination rate is less than what is … Kylie conducts an experiment by randomly selecting 76 seeds of the new brand and plants them. She finds that 70 of those seeds germinated. What are the null and alternative hypotheses for this hypothesis test?**Question:**The owners of a supermarket chain are looking into the effectiveness of the supermarket’s loyalty card program. Specifically, they would like to know if the percentage of shoppers in their stores who use the loyalty card has changed from 63%in 2014. Chloe works in the marketing department of the chain and is … to answer the owners’ inquiry. She randomly selects 196 customers from various stores in the chain and finds that 114 use the loyalty card. What are the null and alternative hypotheses for this hypothesis test?**Question:**A researcher claims that the proportion of college students who plan to participate in community service after graduation is greater than 35%. To test this claim, a survey asked 500randomly selected college students if they planned to perform community service after graduation. Of those students, 195 indicated they planned to perform community service.**Question:**A researcher claims that the proportion of people over 65 years of age in a certain city is greater than 11%. To test this claim, a sample of 1000people are … and its determine that 126 people are over 65 years of age…… The following is the setup for this hypothesis test:…… {H0:p=0.11Ha:p>0.11 ……. Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.**Question:**Rosetta, a pitcher, claims that her pitch speed is more than 57miles per hour, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 1% significance level, to persuade them. She throws 10 The mean speed of the sample pitches is 64 miles per hour. Rosetta knows from experience that the standard deviation for her pitch speed is 4 miles per hour……. H0: μ≤57; Ha: μ>57….. α=0.01 (significance level)…… What is the test statistic (z-score) of this one-mean hypothesis test, … to two decimal places?**Question:**Which of the following results in a null hypothesis p≤0.61and alternative hypothesis p>0.61?**Question:**Suppose the null hypothesis, H0, is: a weightlifting bar can withstand weights of 800pounds and less. What is α, the probability of a Type I error in this scenario?**Question:**Suppose a pitcher claims that his pitch speed is less than 43miles per hour, on average. Several of his teammates do not believe him, so the pitcher decides to do a hypothesis test, at a 10% significance level, to persuade them. He throws 19 The mean speed of the sample pitches is 35 miles per hour. The pitcher knows from experience that the standard deviation for his pitch speed is 6 miles per hour…… H0: μ≥43; Ha: μ<43……α=0.1 (significance level)……. What is the test statistic (z-score) of this one-mean hypothesis test, … to two decimal places?**Question:**Which graph below corresponds to the following hypothesis test?**Question:**Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70%of its customers do not shop at any other sporting goods stores. What is the Type I error in this scenario?**Question:**Which of the following results in a null hypothesis p≥44and alternative hypothesis p<0.44?**Question:**Determine the Type I error if the null hypothesis, H0, is: an electrician claims that no more than 10%of homes in the city are not up to the current electric codes.**Question:**Suppose the null hypothesis, H0, is: the mean age of the horses on a ranch is 6 What is the Type I error in this scenario?**Question:**What is β, the probability of a Type II error if the null hypothesis, H0, is: an electrician claims that no more than 10%of homes in the city are not up to the current electric codes.**Question:**A consumer protection company is testing a towel rack to see how much force it can hold. The null hypothesis, H0, is that the rack can hold at least 100pounds of force. The alternative hypothesis, Ha, is that the rack can hold less than 100pounds of force.**Question:**Suppose the null hypothesis, H0, is: the mean age of the horses on a ranch is 6 What is the Type II error in this scenario?**Question:**Determine the Type I error if the null hypothesis, H0, is: a wooden ladder can withstand weights of 250pounds and less.**Question:**Which of the following answers give valid null and alternative hypotheses for a hypothesis test?**Question:**A mattress store advertises that their beds last at least 5years, on average. A consumer group thinks that they do not last that long and wants to set up a hypothesis test.**Question:**A mechanic wants to show that more than 44%of car owners do not follow a normal maintenance schedule. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p.**Question:**Which of the following results in a null hypothesis p≤0.69and alternative hypothesis p>0.69?**Question:**A city wants to show that the mean number of public transportation users per day is more than 5,575. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ.**Question:**In 2015, the CDC analyzed whether American adults were eating enough fruits and vegetables. Let the mean cups of vegetables adults eat in a day be μ. If the analysts wanted to know if adults were eating, on average, at least the … 2 cups of vegetables a day, what are the null and alternative hypothesis?**Question:**Which of the following results in a null hypothesis p≤0.47and alternative hypothesis p>0.47?**Question:**A hospital claims that the mean wait time for emergency room patients is at least 55 A group of researchers believe that this is not accurate, and want to show that the mean wait time is less than 55minutes. Identify the group’s null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ.**Question:**Which graph below corresponds to the following hypothesis test?**Question:**Which type of test is …. scenario: …… A manufacturer claims that the mean lifetime of a new cutting blade is 2 years. Fourteen blades are randomly … and their lifetime is …. Assume the population follows a normal distributions with known standard deviation.**Question:**Which graph below corresponds to the following hypothesis test?**Question:**Suppose the null hypothesis, H0, is: doctors believe that a surgical procedure is successful at least 80%of the time. Which of the following gives β, the probability of a Type II error?**Question:**Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70%of its customers do not shop at any other sporting goods stores. What is β, the probability of a Type II error in this scenario?**Question:**Determine the Type II error if the null hypothesis, H0, is: the mean price of a loaf of bread is $1.67.**Question:**Which of the following results in a null hypothesis μ≥31and alternative hypothesis μ<31?**Question:**Which of the following results in a null hypothesis μ≤7and alternative hypothesis μ>7?**Question:**A commonly cited study says that 49%of students study less than 5 hours per week. A researcher does not think this is accurate and wants to show that the percentage of students that study less than 5 hours per week is not equal to 49%……. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p.**Question:**Horace, a golfer, claims that his drive distance is less than 225meters, on average. Several of his friends do not believe him, so he decides to do a hypothesis test, at a 10% significance level, to persuade them. He hits 23 The mean distance of the sample drives is 210 meters. Horace knows from experience that the standard deviation for his drive distance is 14meters……. H0: μ≥225; Ha: μ<225……. α=0.1 (significance level)…..What is the test statistic (z-score) of this one-mean hypothesis test, … to two decimal places?**Question:**William, a chef, claims that his meatball weight is not equal to 3ounces, on average. Several of his customers do not believe him, so he decides to do a hypothesis test, at a 1% significance level, to persuade them. He cooks 19 The mean weight of the sample meatballs is 2.9 ounces. William knows from experience that the standard deviation for his meatball weight is 0.5 ounces……. H0: μ=3; Ha: μ≠3…… α=0.01 (significance level)……. What is the test statistic (z-score) of this one-mean hypothesis test, … to two decimal places?

Play Video