Quiz 10.2

A population has µ = 50 and σ = 5. If 10 points are added to every score in the population, then what are the new values for the mean and standard deviation?​

Adding a constant changes the the mean but does not change the standard deviation.

A population of scores has µ = 50 and σ = 5. If every score in the population is multiplied by 3, then what are the new values for the mean and standard deviation?​

If one multiplies every score in a distribution by 3, then the mean and standard deviation are going to multiply by 3 as well.

If sample variance is computed by dividing SS by df = n - 1, then the average value of the sample variances from all the possible random samples will be ____ the population variance.​

If you employ an unbiased formula for sample variance and take the mean of all possible sample variances, then the mean variance should equal the population variance (in theory).

A set of 10 scores has SS = 90. If the scores are a sample, the sample variance is ____ and if the scores are a population, the population variance is ____.​

Sample variance: SS/n-1 Population variance: SS/N

Which set of scores has the smallest standard deviation?​

Standard deviation refers to the average spread of the distribution. A distribution with a small range would have a small standard deviation

There is a six-point difference between two sample means. If the two samples have the same variance, then which of the following values for the variance would make the mean difference easiest to see in a graph showing the two distributions.​

The greater the variance, the more spread out the distribution is and the more difficult it is to tell true difference between two distributions. Therefore, you would want the variances to be small.

The smallest score in a population is X = 5 and the largest score is X = 10. Based on this information, you can conclude that the____.​

The standard deviation is going to be smaller than the range of scores

You have a score of X = 75 on a statistics exam. The mean score for the class on the exam is μ = 70. Which of the following values for the standard deviation would give you the highest position within the class?​

When your score is higher than the mean, you want to get as far as way from the middle group as possible so that you can be the high scoring outlier, a distinguishing high accomplisher. In this case, your score is 75 and the mean is 70. A SD of 5 would mean that you are just part of the 70% middle pack and there is nothing special about you. A SD of 1 means that you are five SDs above the mean, which makes you the top 1% of the population and you are indeed very special. Therefore, you would want the SD to be as small as possible in this case.

You have a score of X = 65 on a math exam. The mean score for the class on the exam is μ = 70. Which of the following values for the standard deviation would give you the most favorable position within the class?​

When your score is lower than the mean, you want to be as close to the mean as possible to be within the 70% of the population in one standard deviation. Therefore, you want the SD to be large enough to include your score. In this case, your score is 65 and the mean is 70. You are five points below the mean. You need a SD greater than 5 so that your score would fall within 1 SD and still be included in the 70% of the population so that you are not an outlier low scorer.