# Business Analytics: Understanding and Using Confidence Intervals

### Understanding and Using Confidence Intervals answers Quiz 1

#### Question 1 of 8A 95% confidence interval is _ to be one that spans the population value than a 99% confidence interval built on the same sample.

• wider and less likely
• narrower and less likely 🗸
• wider and more likely
• narrower and more likely

Question 2 of 8
The standard error of the mean is always smaller than the standard deviation because a single mean has no variability, but the values that the mean consists of do.

• TRUE 🗸
• FALSE

Question 3 of 8
A sample of 16 people has a standard deviation of 20. You plan to take another 16-person sample from the same population. Before you do so, what is your best estimate of the standard deviation of the two sample means?

• 7
• 20
• 1
• 5 🗸

Question 4 of 8
What is the purpose of a confidence interval?

• to find a range of values that, recalculated many times, has a specified probability of being one that includes a population parameter 🗸
• to locate a population parameter along a continuum of values
• to find a range of values that spans a sample statistic
• to find a range of values that has a specified probability of including a population parameter

Question 5 of 8
A 95% confidence interval around a mean extends symmetrically from -2.5 to +1.5. Which of these is a possible outcome if you calculate a 99% confidence interval on the same data?

• The mean moves to 0.0.
• The 99% interval runs from -1.96 to +1.96.
• The 99% interval runs from -3.5 to +1.5 while the mean is unchanged.
• The 99% interval runs from -3.08 to +2.08. 🗸

Question 6 of 8
The distribution of the t-ratio is similar to the normal curve, but the tails of the t-distribution are thicker than the tails of the normal curve. What are the implications for confidence intervals based on t distributions versus normal curves?

• There are no special implications. In either case you need to reach the critical value associated with the confidence level you have chosen.
• You have to go farther into the tails of the t-distribution than into the normal curve’s tails in order to reach a given critical value. The effect you’re testing must be stronger to be regarded as significant by the t ratio. 🗸
• You don’t have to go as far into the tails of the t-distribution than into the normal curve’s tails in order to reach a given critical value. The effect you’re testing must be stronger to be regarded as significant by the normal distribution.

Question 7 of 8
You have measures of the weight in pounds of 16 men. Their mean weight is 100 and the known standard deviation in the population is 15. 90% of the area under the normal curve falls between 1.64 standard deviations above and below the mean. What is the weight of the (hypothetical) man at the 95th percentile of the weight distribution?

• 75.32 pounds
• 130.21 pounds
• 138.64 pounds
• 124.68 pounds 🗸

Question 8 of 8
How do you tell R’s MeanCI function to return a confidence interval based on the normal curve rather than on the t distribution?

• Set the reference = norm argument.
• Omit the SD argument.
• Use the MeanCINorm function rather than the MeanCI function.
• Supply an sd argument that gives the standard deviation based on the degrees of freedom rather than on the actual count. 🗸

### Understanding and Using Confidence Intervals answers Quiz 2

Question 1 of 4
Which of these is closest in concept to using a confidence interval to test the difference between two group means?

• ANOVA
• t-test 🗸
• logistic regression
• Bartlett’s test

Question 2 of 4
Which of these do you need in order to determine the standard error in the confidence interval on the difference between two means?

• the total sum of squares
• the sum of squares between
• the sums of squares within 🗸
• the sum of the absolute deviations

Question 3 of 4
Which of these returns the standard error of the difference between two means?

• the square root of the pooled variance divided by the sum of the sample sizes
• the square root of the sum of squares within times the sum of the reciprocals of the sample sizes
• the square root of the pooled variance times the sum of the reciprocals of the sample sizes 🗸
• the square root of the total variance divided by the total of the sample sizes

Question 4 of 4
How do you present two data samples to the MeanDiffCI function?

• as one data frame with a text vector for group membership and another vector for numeric values
• as two numeric vectors or data frames 🗸
• as the saved results from the ttest function
• as one data frame with two named vectors, one for each sample