1)A manufacturing company produces valves in various sizes and shapes

1)A manufacturing company produces valves in various sizes and shapes. One particular valve plate is supposed to have a tensile strength of 7 pounds per millimeter (lbs/mm). The company tests a random sample of 35 such valve plates from a lot of 125 valve plates (population size N = 125). The sample mean is 6.928 lbs/mm, and the population standard deviation is 0.267 lbs/mm. The company wishes to use a significance level α = .10 to conduct a hypothesis test to determine whether the lot of valve plates has an average tensile strength of 7 lbs/mm. what is the observed value of the test statistic z for the hypothesis test?

2. A restaurant manager collects the data shown below on the number of customers served on 12 randomly selected weekdays. Assuming the number of customers is normally distributed, compute the margin of error of a 90% confidence interval to estimate the average number of customers served by the restaurant on weekdays.

3. A student of business is interested in estimating a 95% confidence interval for the proportion of students who bring laptops to campus. He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within 0.08 points of the population proportion. What is the minimum sample size required by this student, given that a prior estimate of the population proportion is 0.52?
4. Given the information below, enter the p-value to test the following hypothesis at the 1% significance level. What is the p-value for this test?

5. The CEO of a mail order business is reviewing the order filling operations at their two warehouses. The goal is to have 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. To compare the current performance of the warehouses, they decide to conduct a hypothesis test at the 5% significance level. They randomly select 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2). They found that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 365 orders within 24 hours. What is the p-value for testing the hypothesis whether there is a difference in the proportion of shipments at the two warehouses?
6. The diameter of 3.5-inch diskettes is normally distributed. Periodically, quality control inspectors at Dallas Diskettes randomly select a sample of 16 diskettes. If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.59 and 0.08 inches, respectively. Using a 1% significance level, the appropriate decision is
7. An analyst from an energy research institute in Florida wants to estimate the average price of unleaded gasoline in the state. Using a 90% confidence interval. He assumes the standard deviation estimate of $0.22 as reported in the popular press. How many gas stations should he include in his sample to be within $0.07 of the actual average gas price?
8. A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. They ask their realtor friend for help and she informs them that the last 22 houses that sold in their neighborhood took an average time of 229 days to sell. The realtor also tells them that based on her prior experience, the populations standard deviation is 30 days. What is the margin of error of the 95% confidence interval for the mean sale time for all homes in the neighborhood?
9. The water diet requires one to drink two cups of water every half hour from when one gets up until one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. For the population of all adults, assume that the weight loss after six weeks on the diet (weight before beginning the diet – weight after six weeks on the diet) is normally distributed with mean μ. What is the correct hypotheses that must be tested to determine if the diet leads to weight loss?

10. Compute a 95% Confidence Interval for the population proportion given a sample size n = 1000 and a sample proportion = 35%.
11. The diameter of 3.5-inch diskettes is normally distributed. Periodically, quality control inspectors at Dallas Diskettes randomly select a sample of 16 diskettes. If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.54 and 0.08 inches, respectively. Using a 10% significance level, the appropriate decision is
12. A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. They ask their realtor friend for help and she informs them that the last 29 houses that sold in their neighborhood took an average time of 285 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 26 days.  What is the margin of error of the 90% confidence interval for the mean sale time for all homes in the neighborhood?
13. An analyst from an energy research institute in Florida wants to estimate the average price of unleaded gasoline in the state. Using a 90% confidence interval.   He assumes the standard deviation estimate of $ 0.18 as reported in the popular press.  How many gas stations should he include in his sample to be within $ 0.08 of the actual average gas price?

14. A manufacturing company produces valves in various sizes and shapes. One particular valve plate is supposed to have a tensile strength of 6.5 pounds per millimeter (lbs/mm). The company tests a random sample of 35 such valve plates from a lot of 250 valve plates (population size N=250). The sample mean is 6.028 lbs/mm, and the population standard deviation is 0.557 lbs/mm. The company wishes to use a significance level α = .10 to conduct a hypothesis test to determine whether the lot of valve plates has an average tensile strength of 6.5 lbs/mm.  What is the observed value of the test statistic z for the hypothesis test?
15. The CEO of a mail order business is reviewing the order filling operations at their two warehouses.  The goal is to have 100% of orders shipped within 24 hours.  In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. To compare the current performance of the warehouses, they decide to conduct a hypothesis test at the 5% significance level.  They randomly select 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2).  They found that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 365 orders within 24 hours.  What is the p-value for testing the hypothesis that the East Coast Warehouse continues to outperform the West Coast Warehouse?
16. Given the information below, enter the p-value to test the following hypothesis at the 1% significance level. What is the p-value for this test?

17. Compute 99% Confidence Interval for the population proportion given a sample size n = 1000 and a sample proportion = 35%.
18. A student of business is interested in estimating a 95% confidence interval for the proportion of students who bring laptops to campus. He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within 0.04 points of the population proportion. What is the minimum sample size required by this student, given that a prior estimate of the population proportion is 0.49?
19. A restaurant manager collects the data shown below on the number of customers served on 12 randomly selected weekdays. Assuming the number of customers is normally distributed, compute the margin of error of a 95% confidence interval to estimate the average number of customers served by the restaurant on weekdays.

20. An analyst from an energy research institute in Florida wants to estimate the average price of unleaded gasoline in the state. Using a 95% confidence interval. He assumes the standard deviation estimate of $ 0.26 as reported in the popular press.  How many gas stations should he include in his sample to be within $ 0.05 of the actual average gas price?

21. The water diet requires one to drink two cups of water every half hour from when one gets up until one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. For the population of all adults, assume that the weight loss after six weeks on the diet (weight before beginning the diet – weight after six weeks on the diet) is normally distributed with mean μ. To determine if the diet leads to weight loss, we test the hypotheses. Based on these data, what is the p value of the hypothesis test?

22. A restaurant manager collects the data shown below on the number of customers served on 12 randomly selected weekdays. Assuming the number of customers is normally distributed, compute the margin of error of a 90% confidence interval to estimate the average number of customers served by the restaurant on weekdays.

23. The diameter of 3.5-inch diskettes is normally distributed.  Periodically, quality control inspectors at Dallas Diskettes randomly select a sample of 16 diskettes.  If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues.  The last sample showed a mean and standard deviation of 3.54 and 0.08 inches, respectively.  Using a 1% significance level, the appropriate decision is
24. A student of business is interested in estimating a 95% confidence interval for the proportion of students who bring laptops to campus. He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within 0.08 points of the population proportion. What is the minimum sample size required by this student, given that a prior estimate of the population proportion is 0.53?
25. Given the information below, enter the p-value to test the following hypothesis at the 1% significance level. What is the p-value for this test?

26. A restaurant manager collects the data shown below on the number of customers served on 12 randomly selected weekdays. Assuming the number of customers is normally distributed, compute the margin of error of a 99% confidence interval to estimate the average number of customers served by the restaurant on weekdays.

27. The CEO of a mail order business is reviewing the order filling operations at their two warehouses.  The goal is to have 100% of orders shipped within 24 hours.  In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. To compare the current performance of the warehouses, they decide to conduct a hypothesis test at the 5% significance level.  They randomly select 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2).  They found that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 356 orders within 24 hours.  What is the p-value for testing the hypothesis whether there is a difference in the proportion of shipments at the two warehouses?
28. An analyst from an energy research institute in Florida wants to estimate the average price of unleaded gasoline in the state. Using a 90% confidence interval.   He assumes the standard deviation estimate of $ 0.21 as reported in the popular press.  How many gas stations should he include in his sample to be within $ 0.09 of the actual average gas price? 15
29. A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. They ask their realtor friend for help and she informs them that the last 18 houses that sold in their neighborhood took an average time of 208 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 30 days.  What is the margin of error of the 95% confidence interval for the mean sale time for all homes in the neighborhood?
30. A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. They ask their realtor friend for help and she informs them that the last 22 houses that sold in their neighborhood took an average time of 298 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 31 days. What is the margin of error of the 90% confidence interval for the mean sale time for all homes in the neighborhood?