The average income for households in Town 1 is $65,000 with a standard deviation of $30,000....

  

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The average income for households in Town 1 is $65,000 with a standard deviation of $30,000. The average income for households in Town 2 is $60,000 with a standard deviation of $25,000. Suppose a random sample of 50 households is selected from Town I and a random sample of 55 houses is selected from Town 2. (a) What is the shape of the sampling distribution of -? Justify your answer. (b) What are the mean and the standard deviation of the sampling distribution of X,-,? (c) What is the probability that the sample mean from Town 1 is greater than the sample mean from Town 2? (d) To estimate the probability that the sample standard deviation from Town I is greater than the sample standard deviation from Town 2, 100 trials of a simulation were conducted. In each trial, a random sample of size 50 from Town I and a random sample of size 55 from Town 2 was selected and the ratio of their sample standard deviations (s1/s2) was calculated. Use the results of the simulation to estimate the probability that the sample standard deviation from Town 1 is greater than the sample standard deviation from Town 2. Explain how you obtained your estimate. 00 000 0000 0000 000000000 000 000 0 00 0000000000000 000 0.8 1.0 1.2 1.4 1.6 1.8 Simulated sampling distribution of s1/s2 The average income for households in Town 1 is $65,000 with a standard deviation of $30,000. The average income for households in Town 2 is $60,000 with a standard deviation of $25,000. Suppose a random sample of 50 households is selected from Town I and a random sample of 55 houses is selected from Town 2. (a) What is the shape of the sampling distribution of -? Justify your answer. (b) What are the mean and the standard deviation of the sampling distribution of X,-,? (c) What is the probability that the sample mean from Town 1 is greater than the sample mean from Town 2? (d) To estimate the probability that the sample standard deviation from Town I is greater than the sample standard deviation from Town 2, 100 trials of a simulation were conducted. In each trial, a random sample of size 50 from Town I and a random sample of size 55 from Town 2 was selected and the ratio of their sample standard deviations (s1/s2) was calculated. Use the results of the simulation to estimate the probability that the sample standard deviation from Town 1 is greater than the sample standard deviation from Town 2. Explain how you obtained your estimate. 00 000 0000 0000 000000000 000 000 0 00 0000000000000 000 0.8 1.0 1.2 1.4 1.6 1.8 Simulated sampling distribution of s1/s2