The operations manager of a sugar mill in Chesterville wants to estimate the average size ofan order received. An order is measured in the number of pallets shipped from overseas. Arandom sample of 84 orders from customers had a sample mean value of 121.6 pallets.Assume that the population standard deviation is 20 pallets and that order size is normallydistributed. Estimate, with 92% confidence, the mean size of orders received from all the mill’scustomers. A lecturer wants to know if his statistics class has a good grasp of basic maths from matriclevel. Eleven students are chosen at random from the class and given a maths proficiency test.The lecturer wants the class to be able to score above 75 on the test to show that they had agood grasp of basic maths. The eleven students get scores shown below: 62, 88, 71, 50, 67, 70, 92, 75, 6,8 83, 95 Can the lecturer be 95 percent confident that the students had a good grasp of basic maths? 3. A random sample of 200 male shoppers in Pavilion shopping mall were interviewed to identify their reasons for coming to this particular mall. The factor of ‘I prefer Knox brand in the mall’ was the most important reason for 120 of those interviewed. Estimate the likely percentage of all male shoppers who frequent this shopping mall primarily because of the Knox brand inthe mall, using 97.5% confidence limits. 4. The operations manager of a motor vehicle accessories firm with branches in Limpopo and Durban wants to establish whether their Limpopo branch is performing better than their Durban branch in terms of the average size of orders received. Both branches have been operating for only one year. A random sample of 31 orders from the Limpopo branch had an average value of R355.20 with a standard deviation equal to R151.50. Orders received by the Durban branch of the firm were also randomly sampled. The average of the 35 orders sampled was R265.60 with a sample standard deviation of R162.20. Can the operations manager conclude, at the 3% significance level, that the Limpopo branch is performing better than the Durban branch? Show the null and alternative hypotheses for the test and draw the appropriate conclusion. Compute the p-value 5. A farming cooperative in the KwaMashu buys wheat seeds for its farmer members from seed merchants. A particular seed merchant claims that their wheat seeds have at least an 80% germination rate. Before the farming cooperative will buy from this seed merchant, they want to verify this claim. A random sample of 320 wheat seeds supplied by this seed merchant was tested, and it was found that only 230 seeds germinated. Is there sufficient statistical evidence at the 3% significance level to justify the purchase of wheat seeds from this seed merchant? Use the p-value approach to conduct a hypothesis test for a single proportion, and report the findings to the KwaMashu farming cooperative. 6. The width of a confidence interval is a measure of its precision. The narrower the confidence interval, the more precise is the interval estimate, and vice versa. Describe any three aspects that influence the precision of the width of a confidence interval of a single population mean. The average dividend yield of a random sample of 25 JSE-listed companies this year was found to be 14.5%, with a sample standard deviation of 3.4%. Assume that dividend yields are normally distributed. a)Calculate, with 90% confidence, the actual mean dividend yield of all JSE-listed companies this year. Interpret the finding b) Calculate, with 95% confidence, the actual mean dividend yield of all JSE-listed companies this year. Compare the interval with the one calculated in
Hello, Please help me with my statsistics questions:
- The operations manager of a sugar mill in Chesterville wants to estimate the average size ofan order received. An order is measured in the number of pallets shipped from overseas. Arandom sample of 84 orders from customers had a sample
mean value of 121.6 pallets.Assume that the population standard deviation is 20 pallets and that order size is normallydistributed. Estimate, with 92% confidence, the mean size of orders received from all the mill’scustomers. - A lecturer wants to know if his statistics class has a good grasp of basic maths from matriclevel. Eleven students are chosen at random from the class and given a maths proficiency test.The lecturer wants the class to be able to score above 75 on the test to show that they had agood grasp of basic maths. The eleven students get scores shown below:
62, 88, 71, 50, 67, 70, 92, 75, 6,8 83, 95
Can the lecturer be 95 percent confident that the students had a good grasp of basic
maths?
3. A random sample of 200 male shoppers in Pavilion shopping mall were interviewed to identify their reasons for coming to this particular mall. The factor of ‘I prefer Knox brand in the mall’ was the most important reason for 120 of those interviewed. Estimate the likely percentage of all male shoppers who frequent this shopping mall primarily because of the Knox brand inthe mall, using 97.5% confidence limits.
4. The operations manager of a motor vehicle accessories firm with branches in Limpopo and Durban wants to establish whether their Limpopo branch is performing better than their Durban branch in terms of the average size of orders received. Both branches have been operating for only one year. A random sample of 31 orders from the Limpopo branch had an average value of R355.20 with a standard deviation equal to R151.50. Orders received by the Durban branch of the firm were also randomly sampled. The average of the 35 orders sampled was R265.60 with a sample standard deviation of R162.20. Can the operations manager conclude, at the 3% significance level, that the Limpopo branch is performing better than the Durban branch?
Show the null and alternative hypotheses for the test and draw the appropriate conclusion. Compute the p-value
5. A farming cooperative in the KwaMashu buys wheat seeds for its farmer members from seed merchants. A particular seed merchant claims that their wheat seeds have at least an 80% germination rate. Before the farming cooperative will buy from this seed merchant, they want to verify this claim. A random sample of 320 wheat seeds supplied by this seed merchant was tested, and it was found that only 230 seeds germinated. Is there sufficient statistical evidence at the 3% significance level to justify the purchase of wheat seeds from this seed merchant? Use the p-value approach to conduct a hypothesis test for a single proportion, and report the findings to the KwaMashu farming cooperative.
6. The width of a confidence interval is a measure of its precision. The narrower the confidence interval, the more precise is the
a)Calculate, with 90% confidence, the actual mean dividend yield of all JSE-listed companies this year. Interpret the finding
b) Calculate, with 95% confidence, the actual mean dividend yield of all JSE-listed companies this year. Compare the interval with the one calculated in
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