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Statistics > QUESTIONS & ANSWERS > Week 6 Assignment Confidence Interval for Mean - Population Standard Deviation (All)

Week 6 Assignment Confidence Interval for Mean - Population Standard Deviation

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Question Suppose scores of a standardized test are normally distributed and have a known population standard deviation of 11 points and an unknown population mean. A random sample of 15 scores is taken and gives a sample mean of 101 points. Find the confidence interval for the population mean with a 98% confidence level. z0.10 z0.05 z0.02 5 z0.01 z0.00 5 1.28 2 1.64 5 1.96 0 2.32 6 2.57 6 You may use a calculator or the common z values above.  Round the final answer to two decimal places. Question Suppose the weights, in pounds, of the dogs in a city are normally distributed. If the population standard deviation is 3 pounds, what minimum sample size is needed to be 95% confident that the sample mean is within 1 pound of the true population mean? z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576 Use the table above for the z-score, and be sure to round up to the nearest integer. Question Suppose the number of dollars spent per week on groceries is normally distributed. If the population standard deviation is 7 dollars, what minimum sample size is needed to be 90% confident that the sample mean is within 3 dollars of the true population mean? z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576 Use the table above for the z-score, and be sure to round up to the nearest integer. Question School B was interested in finding the population mean of Spanish exam scores across its district. The scores were normally distributed. Based on previous years’ data, the standard deviation was found to be 5 points. The school took a random sample of 25 scores and found the sample mean to be 30. Find a 90% confidence interval estimate for the population mean of Spanish exam scores using the following table and round your answer to four significant figures. z0.1 0 z0.0 5 z0.0 25 z0.0 1 z0.0 05 1.28 2 1.64 5 1.96 0 2.32 6 2.57 6 Question The owner of a factory wants to determine a confidence interval for the average wages at his factory. The population average wages is unknown. However, the owner was able to take a random sample of 64 workers. He found that the average salary for this sample of workers is $50,000. The population standard deviation is $3000. He calculated a 99% confidence interval for the population average wages at the factory. Which of the following choices is correct? Assume the distribution of wages is normally distributed. z0.10 z0.05 z0.02 5 z0.01 z0.00 5 1.28 2 1.64 5 1.96 0 2.32 6 2.57 6

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