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2. A simple random sample of size n is drawn. The sample mean, x ', is found to be 18.4, and the sample standard deviation, 5, is found to be 4.5. (a) Construct a 95% confiden|ce interval for u if the sample size, n, is 35. (b) Construct a 95% confidence interval for u if the sample size, n, is 50. How does increasing the sample size affect the margin of error, E ? (c) Construct a 99% confidence interval for u if the sample size, n, is 35. Compare the results to those obtained in part (a). How does increasing the level of confidence affect the margin of error, E? PART to): Construct a 95% confidence interval for u if the sample size, n, is 35. MANUAL PROCEDURE: The \"6-STEP\" PROCEDURE If\" 5. Step I: What is the sample mean \"17'\" and the sample standard deviation x = ands: 0 Confirm that the sample data come from a simple random sample or randomized experiment. Confirm that the sample size is small relative to the population size (less than 5%). Confirm that either data come from a population that is normally distributed, OR the sample size is large {2 30). Step 3: Choose the critical value tag from Table Vll. tag/2 = Step 4: Compute the standard deviation of the sample mean: 01 = = ? = . Step 5: Compute the \"Margin of Error\": E = {ta/2}{ax) = { }{ } = Step 6: 0 Compute Lower Bound (LB) = x_- E = = 0 Compute Upper Bound (U3) = x'+ E = + = So the 95% confidence interval for p is { , i USING TECHNOLOGY: The "TI83/84 CALCULATOR" PROCEDURE STAT > TESTS Choose (8): "TInterval" DISPLAY: ( PART (b): Construct a 95% confidence interval for u if the sample size, n, is 50. Compare the results to those obtained in part (a). How does increasing the sample size affect the margin of error, E?PART (b): Construct a 95% confidence interval for u if the sample size, n, is 50. Compare the results to those obtained in part (a). How does increasing the sample size affect the margin of error, E? USING TECHNOLOGY: The "TI83/84 CALCULATOR" PROCEDURE STAT > TESTS Choose (8): "TInterval" DISPLAY: ( How does increasing the sample size affect the margin of error, E?PART (c): Construct a 99% confidence interval for u if the sample size, n, is 35. Compare the results to those obtained in part (a). How does increasing the level of confidence affect the margin of error, E? USING TECHNOLOGY: The "TI83/84 CALCULATOR" PROCEDURE STAT > TESTS Choose (8): "TInterval" DISPLAY: ( How does increasing the level of confidence affect the margin of error, E? 4