Hawkes Learning Business Statistics 7.1 Already Graded A

Hawkes Learning Business Statistics 7.1 Already Graded A Decide if the statement is True or False. A sampling distribution of sample means has a standard deviation equal to the population standard deviation, σ. False Can a normal approximation be used for a sampling distribution of sample means from a population with μ=32 and σ=6, when n=9? If the sample size, n, is at least 30 then the shape of a sampling distribution of sample means will approach that of a normal distribution, regardless of the shape of the population distribution. The larger the sample size, the better the normal distribution approximation will be. Therefore, the correct answer is: No, because the sample size is less than 30. Find the mean of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. μ=75 and σ=14; n=36 For any given population, the mean of the sampling distribution of sample means, μx¯ , is equal to the population mean, μ . Therefore: The mean of the sampling distribution of sample means is 75 . Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. μ=40 and σ=8; n=9 For any given population, the standard deviation of the sampling distribution of sample means, σx¯ , is equal to the population standard deviation divided by the square root of the sample size or σ/√n . Therefore: The standard deviation of the sampling distribution of sample means for the given information is 8/√9 or 2.7 Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. μ=51 and σ=9; n=36 9/√36 = 1.5 Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.9 years with a standard deviation of 1.0 years. Step 1 of 2 : If a sampling distribution is created using samples of the ages at which 70 children begin reading, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary. For any given population, the mean of the sampling distribution of sample means, μx¯, is equal to the population mean, μ. Therefore: The mean of the sampling distribution of sampling means is 5.9. Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.9 years with a standard deviation of 1.0 years. Step 2 of 2 : If a sampling distribution is created using samples of the ages at which 70 children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary. For any given population, the standard deviation of the sampling distribution of sample means, σx¯, is equal to the population standard deviation divided by the square root of the sample size or σ√n. Therefore: The standard deviation of the sampling distribution of sampling means for the given information is 1√70 or 0.12. A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 22.7 pounds and a standard deviation of 6.1 pounds. Step 1 of 2 : If a sampling distribution is created using samples of the amounts of weight lost by 70 people on this diet, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary. μ = 22.7 A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 22.7 pounds and a standard deviation of 6.1 pounds. Step 2 of 2 : If a sampling distribution is created using samples of the amounts of weight lost by 70 people on this diet, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary. 6.1√70 = .73 Find the mean of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. μ=45 and σ=8; n=64 μ = 45 Decide if the statement is True or False. The shape of a sampling distribution of sample means that follows the requirements of the Central Limit Theorem will be approximately bell-shaped. True