Statics Probability Questions and Answers
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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.
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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
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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.
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4 :: Sampling distributions tend to be what in shape?

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

Answer: Normal.
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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.
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