MATH 225N Unit 7.1 Developing Hypothesis and understanding Possible Conclusions

MATH 225N Unit 7.1 Developing Hypothesis and understanding Possible Conclusions Question: Which type of test is used in the following scenario: The mean cutting rate of two competing table saws is to be compared. Fourteen cuts are randomly selected and measured for cutting speed to test if the speeds were different from each other. Both populations have normal distributions with known standard deviation. Question Determine the Type I error if the null hypothesis, H0, is: researchers claim that 65% of college students will graduate with debt. Question: A consumer protection company is testing a seat belt to see how much force it can hold. The null hypothesis, H0, is that the seat belt can hold at least 5000 pounds of force. The alternative hypothesis, Ha, is that the seat belt can hold less than 5000pounds of force. What is a Type II error in this scenario? Question A city claims that the mean number of public transportation users per day is at least 4,800. A group of researchers think this is not accurate and want to show that the number of public transportation users is less than 4,800. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ. Question A study claims that the mean age of online dating service users is 40 years. Some researchers think this is not accurate and want to show that the mean age is not 40 years. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ. Question Which of the following results in a null hypothesis p=0.3 and alternative hypothesis p≠0.3? Question A car magazine claims that 68% of car owners follow a normal maintenance schedule. A mechanic does not think this is accurate, and so he wants to show that the percentage of people who follow a normal maintenance schedule is not equal to 68%. 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≤0.48 and alternative hypothesis p0.48? Thus, the car magazine claim should be that the percent is at most 48%, and the mechanic should be trying to show the percent is greater than 48%, which is the second answer choice.   Question: William, a baker, claims that his bread height is more than 13 cm, on average. Several of his customers do not believe him, so he decides to do a hypothesis test, at a 5% significance level, to persuade them. He bakes 17 loaves of bread. The mean height of the sample loaves is 13.9 cm. William knows from experience that the standard deviation for his bread height is 0.7 cm. • H0: μ≤13; Ha: μ13 • α=0.05 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test? Question: Which graph below corresponds to the following hypothesis test? Question: William, a chef, claims that his meatball weight is not equal to 3 ounces, 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 meatballs. 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, rounded to two decimal places? 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 answers give valid null and alternative hypotheses for a hypothesis test? Question: A mattress store advertises that their beds last at least 5 years, on average. A consumer group thinks that they do not last that long and wants to set up a hypothesis test. If μ denotes the average time, in years, that the mattresses last, what are the null and alternative hypotheses in this situation? Question: Which of the following results in a null hypothesis p≤0.47 and alternative hypothesis p0.47? Question: Which of the following results in a null hypothesis p≤0.69 and alternative hypothesis p0.69? 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: Marketers at PaperClips, a regional office supply chain, are researching whether the population mean amount spent on back-to-school shopping for students in grades K–12 has changed from 2016 to 2018. Based on market research, the marketers assume that the population standard deviation is $101.52 for 2016 and $96.47 for 2018. Households across the region with at least one student in grades K–12 were randomly selected in 2016 and again in 2018. The results are shown in the table below. Explain whether a hypothesis test for the difference between two means of independent samples is appropriate, and if so, find the null and alternative hypotheses, where μ1 is the population mean amount spent on back-to-school shopping per household in 2016 and μ2 is the population mean amount spent on back-to-school shopping per household in 2018. Question: Leah Peschel is the bottling department manager for a bottling company that produces various soft drinks and juices. The company uses two different machines from different manufacturers to fill the bottles of its popular cola. Leah periodically verifies that the population mean amount of cola in the bottles filled by Machine 1 is the same as the population mean amount in the bottles filled by Machine 2. The manufacturers calibrated the machines at the time of installation and provided that information to the bottling company. Based on this information, Leah assumes that the population standard deviation for Machine 1 is 0.021 ounce and the population standard deviation for Machine 2 is 0.019 ounce. Leah randomly selects samples of bottles filled by Machine 1 and Machine 2. The amount of cola in each bottle is recorded for both samples, and the results are shown in the table. Explain whether a hypothesis test for the difference between two means of independent samples is appropriate, and if so, find the null and alternative hypotheses, where μ1 is the population mean of Machine 1 and μ2 is the population mean of Machine 2. Question: A team of archeologists is reexamining a site where two additional sets of artifacts have been discovered. The sets of artifacts are in two separate areas of the archeological site, where each set is adjacent to artifacts that were discovered in the past. Since both sets of artifacts were discovered at about the same time years after the first examination, the members of the team would like to find out whether the population mean age of the artifacts in set A is the same as the population mean age of the artifacts in set B. Using information from the first examination of the site, the team assumes that the population standard deviation of the age of the artifacts found in set A is 135 years and the population standard deviation of the age of the artifacts found in set B is 119 years. The team takes a random sample of the artifacts and finds the ages of each artifact using radiocarbon dating. The sample results are provided in the table below. Explain whether a hypothesis test for the difference between two means of independent samples is appropriate, and if so, determine the null and alternative hypotheses for this hypothesis test, where μ1 is the population mean age, in years, of the artifacts in set A and μ2is the population mean age, in years, of the artifacts in set B.   Question: Simone Lahey is a district vice president of a bank. She is receiving complaints from bank customers about the amount of time they have to wait in the Mineola branch. She is investigating whether the population mean wait time of the Mineola branch is greater than the population mean wait time of the Westbury branch. Simone carefully reviews studies of the mean wait times conducted in the past and assumes that the population standard deviation is 1.09 minutes in the Mineola branch and 0.96 minute in the Westbury branch. Simone conducts a survey at each branch over a period of time by randomly selecting customers who wait in line and then recording each customer’s wait time in minutes. The results of the survey are displayed in the table shown below. Explain whether a hypothesis test for the difference between two means of independent samples is appropriate, and if so, determine the null and alternative hypotheses for this hypothesis test. Let μ1be the population mean wait time for customers in the Mineola branch and μ2 be the population mean wait time for customers in the Westbury branch. Question: Calculate the test statistic for the difference between the means, μ1−μ2, from the following summary statistics for the hypothesized difference D0=0. Question: Leah Peschel is the bottling department manager for a bottling company that produces various soft drinks and juices. The company uses two different machines from different manufacturers to fill the bottles of its popular cola. Leah periodically verifies that the population mean amount of cola in the bottles filled by Machine 1 is the same as the population mean amount in the bottles filled by Machine 2. The manufacturers calibrated the machines at the time of installation and provided that information to the bottling company. Based on this information, Leah assumes that the population standard deviation for Machine 1 is 0.021 ounce and the population standard deviation for Machine 2 is 0.019 ounce. Leah randomly selects samples of bottles filled by Machine 1 and Machine 2. The amount of cola in each bottle is recorded for both samples, and the results are shown in the table. Let μ1 be the population mean of Machine 1 and μ2 be the population mean of Machine 2. What type of test is this hypothesis test? Answer: This is a two-tailed test because the alternative hypothesis is Ha:μ1−μ2≠0. Leah is testing whether the amount of cola in the bottles filled by Machine 1 is the same as the amount in the bottles filled by Machine 2, which would be the null hypothesis in this case. She is looking for evidence that supports μ1 not being equal to μ2. Therefore, the alternative hypothesis is Ha:μ1−μ2≠0, which means that this hypothesis test is a two-tailed test. Question: Marketers at PaperClips, a regional office supply store, are researching whether the population mean amount spent on back-to-school shopping for students in grades K–12 has changed from 2016 to 2018. Based on market research, the marketers assume that the population standard deviation is $101.52 for 2016 and $96.47 for 2018. Households across the region with at least one student in grades K–12 were randomly selected in 2016 and again in 2018. The results are shown in the table below. Let μ1 be the population mean amount spent on back-to-school shopping per household in 2016 and μ2 be the population mean amount spent on back-to-school shopping per household in 2018. What type of test is this hypothesis test? Question: What is/are the critical value(s) of the z-test statistic for this hypothesis test, where α=0.05? Use the appropriate value(s) from the table. Use a comma and a space to separate answers as needed. Question: Suppose a baker claims that her bread height is more than 13 cm, on average. Several of her customers do not believe her, so the baker decides to do a hypothesis test, at a 10% significance level, to persuade them. She bakes 25 loaves of bread. The mean height of the sample loaves is 13.8 cm. The baker knows from experience that the standard deviation for her bread height is 0.9 cm. • H0: μ≤13; Ha: μ13 • α=0.1 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? . Question: Olivia, a golfer, claims that her drive distance is more than 174 meters, on average. Several of her friends do not believe her, so she decides to do a hypothesis test, at a 10% significance level, to persuade them. She hits 15 drives. The mean distance of the sample drives is 188 meters. Olivia knows from experience that the standard deviation for her drive distance is 14meters. • H0: μ≤174; Ha: μ174 • α=0.1 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?