1 Distinguish Between Point And Interval Estimate In Inferential Statistics 1 2 For Each Of The Following Cases Fin 1 (62.12 KiB) Viewed 60 times
1 Distinguish Between Point And Interval Estimate In Inferential Statistics 1 2 For Each Of The Following Cases Fin 2 (67.75 KiB) Viewed 60 times
1. Distinguish between point and interval estimate in inferential statistics. (1) 2. For each of the following cases find the t value a) Sample size of 15 with a confidence level of 95% (1) b) Sample size of 6 with a confidence level of 90% c) Sample size of 20 with a confidence level of 99% (1) 3. Suppose UBER, a South African based car rental firm, wishes to estimate the average number of miles traveled per day by each of its cars rented in Cape Town. A random sample of 20 cars rented in Cape Town reveals that the sample mean travel distance per day is 85.5 miles, with a population standard deviation of 19.3 miles. Assume that number of miles traveled per day is normally distributed in the population. Compute a 99% confidence interval to estimate the population mean. (4) (2) 4. A sample of 250 observations is selected from a normal population with a population standard deviation of 25. The sample mean is 20. a) Determine the standard error of the mean. b) Determine the 95% confidence interval for the population mean. (3) c) Justify why you chose the formula used in part b above to determine the 95% confidence interval (1) 5. Shoprite stores wishes to determine the proportion of customers who pay for their goods purchased at their stores using ATM cards. The company surveys 100 customers and finds that 80 paid using ATM cards. a) Estimate the value of the population proportion. (1) b) Develop a 95% confidence interval for the population proportion (3) c) Interpret your findings. (1)
6. A research firm conducted a survey of 49 randomly selected Zambian employees to determine the mean amount spent on coffee during a week. The sample mean was K20 per week. The population distribution is normal with a standard deviation of K. a) What is the point estimate of the population mean? Explain what it indicates. (1) b) Using the 95% level of confidence, determine the confidence interval for the unknown population mean. (3) c) Interprete your answer in part b above. (1) d) Is the assumption that the underlying population of measurements is normally distributed necessary to ensure the validity of the confidence interval calculated in part b above? Explain. (1) II 7. The owner of Honda eggs farm wants to estimate the mean number of eggs laid per chicken. A sample of 20 chickens shows they laid an average of 20 eggs per month with a standard deviation of 2 eggs per month a. Determine the point estimate for the population mean. (1) b. Develop a 95% confidence interval for the population mean of eggs. c. Would it be reasonable to conclude that the population mean is 21 eggs? Justify your answer. (1) 8. Assuming that a high school graduate recently assumed the position of a farmer union representative in a certain community. He would like some data on how long current members of the farmer union group have been members. To investigate suppose he selects a random sample of 40 current members. The mean length of membership for the sample is 8.32 years and the standard deviation is 3.07 years. a) Develop a 90% confidence interval for the population mean (3) b) The previous representative, in the summary report she prepared for handover, indicated the mean length of membership was now almost 10 years." Does the sample information substantiate this claim? Explain. (1)
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