Timmy could follow two main routes to get to school. Timmy believes that route 1 is faster than route 2. To investigate, he decides to keep track for the next 4 weeks. Each morning, he flips a coin to determine which route he takes. Of the 20 school days, 12 days were randomly assigned to route 1, and 8 days were randomly assigned to route 2. The mean travel time for days assigned to route 1 was 20 minutes with a standard deviation of 3 minutes. The mean travel time for the days assigned to route 2 was 22 minutes with a standard deviation of 2 minutes. Let mu sub 1 is equal to the true mean travel time to school along route 1 and mu sub 2 is equal to the true mean travel time to school along route 2. Timmy would like to know if the data provide convincing evidence of a difference in travel time for the 2 routes. Dotplots of the distribution of travel time for route 1 and route 2 show no strong skewness or outliers. What are the appropriate hypotheses?
An auto body shop receives 70 percent of its parts from one manufacturer. If parts from the shop are selected at random with replacement, what is the probability that the first part not from this manufacturer is the 6 th part selected?
A therapist wanted to determine if yoga or meditation is better for relieving stress. The therapist recruited 100 of her high-stress patients. Fifty of them were randomly assigned to take weekly yoga classes, and the other 50 were assigned weekly meditation classes. After one month, 30 of the 50 patients in the yoga group reported less stress, and 35 of the 50 patients in the meditation group reported less stress. Assuming the conditions for inference are met, what is the 95 percent confidence interval for the difference in proportions of patients experiencing stress relief from the yoga and meditation groups? Use the z -table.
A social worker at a large high school wants to estimate the number of days students are absent. He randomly selects 45 students and records the number of days each one is absent. The social worker constructs a 95 percent confidence interval for the true mean number of days students at this school are absent. Which of the following would decrease the margin of error?
The amount of time it takes students to travel to school can vary greatly depending on how far a student lives from the school and what mode of transportation they take to school. A student claims that the average travel time to school for his large district is 20 minutes. To further investigate this claim, he selects a random sample of 50 students from the school and finds that their mean travel time is 22 point 4 minutes with a standard deviation of 5 point 9 minutes. He would like to conduct a significance test to determine if there is convincing evidence that the true mean travel time for all students who attend this school is greater than 20 minutes. The student would like to test ratio of cap h sub 0 to mu is equal to 20 versus ratio of cap h sub A to mu is greater than 20 , where mu is equal to the true mean travel time for all students who attend this school. The conditions for inference are met. What are the appropriate test statistic and cap p -value? Use the t -table.
A random sample of 100 customers is selected, and the mean difference in their satisfaction rating for company A and company B is calculated. A rating of 1 indicates that a customer is highly dissatisfied, and a rating of 5 indicates that a customer is highly satisfied. A 90 percent confidence interval for the true mean difference (company A – company B) in satisfaction ratings is negative 2 point 5 to 1 point 5 Based on the confidence interval, the owner of company B claims that customers are more satisfied with his company than with company A. Is this claim supported by the 90 percent confidence interval?
A student at a large high school selects a random sample of 145 students. For each, she records the grade level and their favorite color. She would like to know if there is convincing evidence that grade level is associated with favorite color. Let alpha is equal to 0 point 0 5 What are the hypotheses for this test?
The mean weight for a typical bunch of bananas in grocery stores is 3 point 5 4 pounds. The owner of a grocery store will reject a shipment of bananas if the mean weight of the banana bunches is less than 3 point 5 4 pounds. The owner randomly selects and weighs 30 bunches of bananas. A significance test at an alpha level of alpha is equal to 0 point 0 5 tests the hypotheses ratio of cap h sub 0 to mu is equal to 3 point 5 4 pounds; ratio of cap h sub alpha to mu is less than 3 point 5 4 pounds. What is a Type II error in this situation?
A conference consists of 5 sessions: A, B, C, D, and E. Here are the costs of the sessions. Session A: $50 Session B: $50 Session C: $100 Session D: $150 Session E: $200 A participant plans to attend 3 sessions. Which of the following gives a complete list of all possible samples of size 3 from this population of 5 sessions, selected without replacement?
A political pollster claims that 55 percent of voters prefer candidate A. To investigate this claim, a random sample of 75 voters is polled. The pollster finds that 39 of those polled prefer candidate A. He would like to know if the data provide convincing evidence that the true proportion of all voters who prefer candidate A is less than 55 percent What are the values of the test statistic and cap p -value for this test? Use the z -table.
What critical value of t to the th power times should be used for a 99 point 5 percent confidence interval for the population mean based upon a random sample of 18 observations? Use the t -table.
The mayor of a large town wants to estimate the proportion of households in the town that would support a proposal. The mayor’s assistant randomly selects 100 households and asks whether they would support the mayor’s proposal. Sixty households responded that they would. What is the appropriate inference procedure?
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