Use the grey star to mark the mean of the sample. (Be sure to place the star on

Question

Use the grey star to mark the mean of the sample. (Be sure to place the star on the horizontal blue line segment that represents the confidence interval.) To construct the confidence interval, the quantity t_SM is subtracted from and added to the sample mean. In this case, t_SM =. Suppose that the researcher uses the same sample but decides to construct a 85% confidence interval of the mean of the population. Compared with the center of the 95% confidence interval, the center of the 85% confidence interval _____. Compared to the 95% confidence interval, the 85% confidence interval ____. At the same confidence level, _____ in the sample size would have a similar effect on the width of the confidence interval as changing the confidence level from 95% to 85%.

Explanation / Answer

tsM = t-value * Standard Error of Mean is subtracted from mean to get the lower interval and the same is added to the sample mean to get the upper interval.

Here, the centre of the blue horizontal line will the sample mean which is equal to 26.5. And, we also have upper confidence interval = 30 and lower confidence interval = 23. Hence, tsM = 26.5 - 23 = 3.5

tsM = 3.5

Compared with the center of the 95% confidence interval, the center of the 85% confidence interval will not change. Because, the center of the confidence interval is sample mean, which will be the same for any confidence intervals.

Compared to 95% confidence interval, the 85% confidence interval will be narrower. Becuase, the t-value for the 85% CI will be lesser than the 95% confidence interval. Hence, the factor tsM will be reduced resulting in the narrower CI.

At the same confidence level, increment in the sample size would have a similar effect on the width of the confidence interval as changing the confidence level from 95% to 85%. Becuase, as the sample size increases the standard error of the mean sM will decrease. Hence, the factor tsM will be reduced resulting in the narrower CI.

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