Fresh Statics Probability Interview Questions & Answers:

1. There is substantial overlap between two sets of confidence intervals on an error bar chart. The chart shows confidence intervals for boys and girls on a depression questionnaire. What could we make of this?

1. We can be 95% confident that the population means are within the intervals indicated on the chart. As there is much overlap between the two sets of confidence intervals we cannot be sure whether there is a difference in the population means. It seems likely that there is no difference but we cannot draw any firm conclusions.
2. We can be 95% confident that the population means are within the intervals indicated on the chart. As there is much overlap between the two sets of confidence intervals this would suggest that there is a real difference in the population means.
3. It would appear that 95% of girls are more depressed than boys according to the confidence intervals.
4. We can be 5% confident that the population means are within the intervals indicated on the chart. As there is much overlap between the two sets of confidence intervals we can be sure that there is a real difference in the population means.

Answer: We can be 95% confident that the population means are within the intervals indicated on the chart. As there is much overlap between the two sets of confidence intervals we cannot be sure whether there is a difference in the population means. It seems likely that there is no difference but we cannot draw any firm conclusions.

2. In error bar charts the larger the confidence interval the _____ the line is through the mean.

1. More curved
2. More overlapping
3. Shorter
4. Longer

Answer: longer

3. Which of the following is the correct statement?

1. The standard error of the sampling distribution of the mean tells us how much our samples tend to vary around the population mean.
2. The standard deviation of the sampling distribution is called the sampling error.
3. The mean of several sample means gives the best estimate of the population means.
4. The larger the sampling size the larger the sampling error.

Answer: The mean of several sample means gives the best estimate of the population means.

4. Sampling distributions tend to be what in shape?

1. Bimodal.
2. Positively skewed.
3. Normal.
4. Flat.

Answer: Normal.

5. Which of the following type of graph can display confidence intervals?

1. Venn diagrams.
2. Histograms.
3. Error bar charts.
4. Regression lines.

Answer: Error bar charts.

6. A sample mean is a ____ estimate and we do not know how close it is to the population mean.

1. Confidence
2. Point
3. Sample
4. Distribution

Answer: point

7. To calculate confidence intervals we need make use of:

1. Sampling distributions.
2. Histograms.
3. z-scores.
4. None of the above.

Answer: sampling distributions.

8. The standard error has been calculated as 2.6 and the sample mean is 10.00. Thus the 95% confidence interval lies between:

1. 4.904 to 15.096
2. 7.40 to 12.60
3. 3.85 to 26
4. There is not enough information available to work out the confidence interval.

Answer: 4.904 to 15.096

9. In another study you have a standard deviation of 12, a mean of 20 and a sample size of 50. What is the standard error?

1. 0.089
2. 0.069
3. 1.7
4. 0.589

Answer: 1.7

10. Finally, you still have the same data (a sample size of 7, a mean of 8 and a standard deviation of 4.2) plus the standard error and you know how to calculate the 95% confidence interval. Thus what is the 95% confidence interval?

1. 2.80 to 10.80
2. 3.36 to 11.36
3. 4.90 to 11.10
4. 3.98 to 11.98

Answer: 4.90 to 11.10