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 4.9 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 8.56 to 10.19 and the mean is known to be 9.375, what is the margin of error? 3. Question:(CO 4) If the population standard deviation of a sample increases without other changes, what is most likely to happen to the confidence interval? 4. Question:(CO 4) From a random sample of 41 teens, it is found that on average they spend 43.1 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 12.10 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 4.82 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 fifteen 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 0.09 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 20.48 to 21.02. What conclusion can be made? 14. Question:(CO 4) In a sample of 15 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 known rather than the sample standard deviation, what would be the impact on the confidence interval? 16. Question:(CO 5) A company claims that its heaters last less than 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 less than 2.5 hours each week in meetings. Write the null and alternative hypotheses and note which is the claim. 18. Question:(CO 5) In hypothesis testing, a key element in the structure of the hypotheses is that the claim is ________________________. 19. Question:(CO 5) A landscaping company claims that at least 90% of workers arrive on time. If a hypothesis test is performed that rejects 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 80 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 280.7 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 standard deviation 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 4.1 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 6.812 inches with a population standard deviation of 0.03 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 threestar hotel rooms in Chicago, the mean room rate is $165 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 1.1 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=0.01, 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 $1930. 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?