A simple random sample of size n is drawn. The sample mean, x overbar, is found to be 17.6, and the sample standard deviation, s, is found to be 4.1. LOADING... Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about mu if the sample size, n, is 35. Lower bound: nothing; Upper bound: nothing (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about mu if the sample size, n, is 51. Lower bound: nothing; Upper bound: nothing (Use ascending order. Round to two decimal places as needed.) How does increasing the sample size affect the margin of error, E? A. The margin of error does not change. B. The margin of error increases. C. The margin of error decreases. (c) Construct a 99% confidence interval about mu if the sample size, n, is 35. Lower bound: nothing; Upper bound: nothing (Use ascending order. Round to two decimal places as needed.) Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? A. The margin of error does not change. B. The margin of error decreases. C. The margin of error increases. (d) If the sample size is 16, what conditions must be satisfied to compute the confidence interval? A. The sample data must come from a population that is normally distributed with no outliers. B. The sample size must be large and the sample should not have any outliers. C. The sample must come from a population that is normally distributed and the sample size must be large. Click to select your answer(s)
a)
sample mean 'x̄= | 17.600 |
sample size n= | 35.00 |
sample std deviation s= | 4.100 |
for 95% CI; and 34 df, value of t= | 2.0320 | |
margin of error E=t*std error = | 1.408 | |
lower bound=sample mean-E = | 16.19 | |
Upper bound=sample mean+E = | 19.01 |
b)
for 95% CI; and 50 df, value of t= | 2.0090 | |
margin of error E=t*std error = | 1.153 | |
lower bound=sample mean-E = | 16.45 | |
Upper bound=sample mean+E = | 18.75 |
. C. The margin of error decreases
c)
for 99% CI; and 34 df, value of t= | 2.7280 | |
margin of error E=t*std error = | 1.891 | |
lower bound=sample mean-E = | 15.71 | |
Upper bound=sample mean+E = | 19.49 | |
C. The margin of error increases.
d)
A. The sample data must come from a population that is normally distributed with no outliers.
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