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Question 14A random sample of 61 Basic Statistics students were asked what they thought of statistics on a scale of 0 (very stupid) to 100 (very nice). Interestingly, students seem to find statistics quite nice: the sample mean equals 83. The sample standard deviation equals 7. We know that the standard deviation in the population (all BS students) is 8. Calculate the 90% confidence interval. 1 point(81.53, 84.47) (81.24, 84.76) (81.32, 84.68) (80.99, 85.01)

Question

Question 14A random sample of 61 Basic Statistics students were asked what they thought of statistics on a scale of 0 (very stupid) to 100 (very nice). Interestingly, students seem to find statistics quite nice: the sample mean equals 83. The sample standard deviation equals 7. We know that the standard deviation in the population (all BS students) is 8. Calculate the 90% confidence interval. 1 point(81.53, 84.47) (81.24, 84.76) (81.32, 84.68) (80.99, 85.01)

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Solution

To calculate the 90% confidence interval, we first need to find the standard error (SE). Since we know the standard deviation of the population (σ), we can use it to calculate the standard error. The formula for the standard error when the population standard deviation is known is σ/√n, where n is the sample size.

In this case, σ = 8 and n = 61.

SE = 8/√61 = 1.02

Next, we need to find the z-score that corresponds to a 90% confidence level. The z-score for a 90% confidence level is approximately 1.645 (you can find this value in a standard z-table or using a calculator).

The margin of error (ME) is then calculated as the z-score times the standard error.

ME = 1.645 * 1.02 = 1.68

Finally, we calculate the confidence interval by subtracting the margin of error from the sample mean for the lower limit and adding the margin of error to the sample mean for the upper limit.

Lower limit = 83 - 1.68 = 81.32 Upper limit = 83 + 1.68 = 84.68

So, the 90% confidence interval for the mean score is approximately (81.32, 84.68).

This problem has been solved

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