A 95 % confidence interval for the population standard deviation is given by ( ) 50.74 39.08 20.17 81.57 57.17 77.74 76.27 42.66 82.06 77.57 87.11 56.48 68.57 63.45 66.79 48.34 26.29 25.05 51.04 48.4 54.54 64.02 43.43 56.19 64.92 99.31 59.78 47.05 42.18 63.33 45.84 89.07 51.57 80.92 39.1 51.19 70.17 59.31 76.17 40.5 57.56 59.42 74.11 89.14 51.17 39.33 70.91 70.89 64.26 67.68 37.09 57.62 61.69 50.74 55.4 90.77 50.66 100.91 57.28 37.32 38.7 52.86 56.39 29.65 78.7 53.45 41.47 38.23 61.15 99.24 74.87 52.02 63.1 44.76 31.55 76.4 16.04 28.42 67.92 60.71 56.55 82.69 70.31 57.16 24.28 69.77 54.48 75.25 64.05 24.49 39 72.32 70.22 35.77 61.17 51.32 64.76 105.23 66.13 19.99
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Step 1:** Calculate the degrees of freedom: \(n - 1 = 100 - 1 = 99\) ** Show more…
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Construct a confidence interval of the population proportion at the given level of confidence x=860, n=1100, 95% confidence Click here to view the standard normal distribution The lower bound of the confidence interval is (Round to three decimal places as needed.) The upper bound of the confidence interval is (Round to three decimal places as needed.)
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Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 19 mortgage institutions, the mean interest rate was 3.57% and the standard deviation was 0.43%. Assume the interest rates are normally distributed. Which distribution should be used to construct the confidence interval? A. Use a normal distribution because n < 30 and the interest rates are normally distributed. B. Use a normal distribution because the interest rates are normally distributed and ̃ is known. C. Use a t-distribution because the interest rates are normally distributed and ̃ is known. D. Use a t-distribution because it is a random sample, ̃ is unknown, and the interest rates are normally distributed. E. Cannot use the standard normal distribution or the t-distribution because ̃ is unknown, n < 30, and the interest rates are not normally distributed. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. A. The 95% confidence interval is ( , ). (Round to two decimal places as needed.) B. Neither distribution can be used to construct the confidence interval. Interpret the results. Choose the correct answer below. A. It can be said that 95% of institutions have an interest rate between the bounds of the confidence interval. B. If a large sample of institutions are taken approximately 95% of them will have an interest rate between the bounds of the confidence interval. C. With 95% confidence, it can be said that the population mean interest rate is between the bounds of the confidence interval. D. Neither distribution can be used to construct the confidence interval.
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