MATH 221 Week 7 Quiz

1. Question: (CO 4) From a random sample of 55 businesses, it is found that the mean time that employees spend on personal issues each week is 5.8 hours with a standard deviation of 0.35 hours. What is the 95% confidence interval for the amount of time spent on personal issues? 2. Question: (CO 4) If a confidence interval is given from 8.52 to 10.23 and the mean is known to be 9.375, what is the margin of error? 3. Question: (CO 4) Which of the following is most likely to lead to a small margin of error? 4. Question: (CO 4) From a random sample of 85 teens, it is found that on average they spend 31.8 hours each week online with a population standard deviation of 5.91 hours. What is the 90% confidence interval for the amount of time they spend online each week? 5. Question: (CO 4) A company making refrigerators strives for the internal temperature to have a mean of 37.5 degrees with a population standard deviation of 0.6 degrees, based on samples of 100. A sample of 100 refrigerators have an average temperature of 37.70 degrees. Are the refrigerators within the 90% confidence interval? 6. Question: (CO 4) What is the 97% confidence interval for a sample of 104 soda cans that have a mean amount of 12.05 ounces and a population standard deviation of 0.08 ounces? 7. Question: (CO 4) Determine the minimum sample size required when you want to be 98% confident that the sample mean is within two units of the population mean. Assume a population standard deviation of 5.75 in a normally distributed population. 8. Question: (CO 4) Determine the minimum sample size required when you want to be 80% confident that the sample mean is within 1.3 units of the population mean. Assume a population standard deviation of 9.24 in a normally distributed population 9. Question: (CO 4) Determine the minimum sample size required when you want to be 75% confident that the sample mean is within twenty-five units of the population mean. Assume a population standard deviation of 327.8 in a normally distributed population 10. Question: (CO 4) In a sample of 8 high school students, they spent an average of 28.8 hours each week doing sports with a sample standard deviation of 3.2 hours. Find the 95% confidence interval, assuming the times are normally distributed. 11. Question: (CO 4) In a sample of 15 stuffed animals, you find that they weigh an average of 8.56 ounces with a sample standard deviation of 0.07 ounces. Find the 92% confidence interval, assuming the times are normally distributed 12. Question: (CO 4) Market research indicates that a new product has the potential to make the company an additional $3.8 million, with a standard deviation of $1.9 million. If this estimate was based on a sample of 10 customers from a normally distributed data set, what would be the 90% confidence interval? 13. Question: (CO 4) Supplier claims that they are 95% confident that their products will be in the interval of 20.45 to 21.05. You take samples and find that the 95% confidence interval of what they are sending is 20.02 to 21.48. What conclusion can be made? 14. Question: (CO 4) In a sample of 18 small candles, the weight is found to be 3.72 ounces with a standard deviation of 0.963 ounces. What would be the 87% confidence interval for the size of the candles, assuming the data are normally distributed? 15. Question: (CO 4) In a situation where the population standard deviation was decreased from 5.8 to 3.1, what would be the impact on the confidence interval? 16. Question: (CO 5) A company claims that its heaters last at most 5 years. Write the null and alternative hypotheses and note which is the claim. 17. Question: (CO 5) An executive claim that her employees spend no less than 2.5 hours each week in meetings. Write the null and alternative hypothesesand note which is the claim. 18. Question: (CO 5) In hypothesis testing, a key element in the structure of the hypotheses is that the null hypothesis has the ________________________. 19. Question: (CO 5) A landscaping company claims that at most 90% of workers arrive on time. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted? 20. Question: (CO 5) A textbook company claims that their book is so engaging that more than 55% of students read it. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted? 21. Question:(CO 5) An advocacy group claims that the mean braking distance of a certain type of tire is 75 feet when the car is going 40 miles per hour. In a test of 45 of these tires, the braking distance has a mean of 77 and a population standard deviation of 5.9 feet. Find the standardized test statistic and the corresponding p-value. 22. Question:(CO 5) The heights of 82 roller coasters have a mean of 284.9 feet and a population standard deviation of 59.3 feet. Find the standardized tests statistics and the corresponding p-value when the claim is that roller coasters are less than 290 feet tall. 23. Question:(CO 5) A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 720 hours. A random sample of 51 light bulbs as a mean of 705.4 hours with a population standarddeviation of 62 hours. At an α=0.05, can you support the company’s claim using the test statistic? 24. Question:(CO 5) A restaurant claims the customers receive their food in less than 16 minutes. A random sample of 39 customers finds a mean wait time for food to be 15.8 minutes with a population standard deviation of 4.9 minutes. At α = 0.04, can you support the organizations’ claim using the test statistic? 25. Question:(CO 5) A manufacturer claims that their calculators are 6.800 inches long. A random sample of 39 of their calculators finds they have a mean of 6.810 inches with a population standard deviation of 0.05 inches. At α=0.08, can you support the manufacturer’s claim using the p value? 26. Question:(CO 5) A travel analyst claims that the mean room rates at a three-star hotel in Chicago is greater than $152. In a random sample of 36 three-star hotel rooms in Chicago, the mean room rate is $159 with a population standard deviation of $41. At α=0.10, can you support the analyst’s claim using the p-value? 27. Question:(CO 5) A car company claims that the mean gas mileage for its luxury sedan is at least 24 miles per gallon. A random sample of 7 cars has a mean gas mileage of 23 miles per gallon and a standard deviation of 1.2 miles per gallon. At α=0.05, can you support the company’s claim assuming the population is normally distributed? 28. Question:(CO 5) A state Department of Transportation claims that the mean wait time for various services at its different location is more than 6 minutes. A random sample of 16 services at different locations has a mean wait time of 9.5 minutes and a standard deviation of 7.6 minutes. At α=0.05, can the department’s claim be supported assuming the population is normally distributed? 29. Question:(CO 5) A used car dealer says that the mean price of a three-year-old sport utility vehicle in good condition is $18,000. A random sample of 20 such vehicles has a mean price of $18,450 and a standard deviation of $1050. At α=0.08, can the dealer’s claim be supported assuming the population is normally distributed? 30. Question:(CO 5) A researcher wants to determine if eating more vegetables helps high school juniors learn algebra. One junior class has extra vegetables and another junior class does not. After 2 weeks, the entire both classes take an algebra test and the results of the two groups are compared. To be a valid matched pair test, what should the researcher consider in creating the two groups?