### Sample Variance, Distribution, Small Sample Size – Statistics

The key terms in these Statistics chapters include Sample Variance, Population, Distribution, Small Sample Size – Statistics

If other factors are held constant, which set of sample characteristics is most likely to reject a null hypothesis stating that M = 80?

**M = 90 and small sample variance**

When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution?**It is flatter and more spread out than the normal distribution.**

A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df = 30, how many individuals were in the sample?

**n = 31**

With α = .01, the two-tailed critical region for a t test using a sample of n= 16 subjects would have boundaries of ______.

**t = ±2.947**

On average, what value is expected for the t statistic when the null hypothesis is true?

**0**

For a population with μ=100 and σ=20, what is the X value corresponding to z=-0.75?

**85**

**x = μ+zσ**

Under what circumstances is a score that is located 5 points above the mean a central value, relatively close to the mean?

**When the population standard deviation is much greater than 5**

On the exam with μ=52, you have a score of x=44. Which value for the standard deviation would give you the highest position in the class distribution?

**σ = 8**

If other factors are held constant, which set of sample characteristics is most likely to reject a null hypothesis stating that M = 80?

**M = 90 and small sample variance**

When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution?**It is flatter and more spread out than the normal distribution.**

A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df = 30, how many individuals were in the sample?

**n = 31**

With α = .01, the two-tailed critical region for a t test using a sample of n= 16 subjects would have boundaries of ______.

**t = ±2.947**

On average, what value is expected for the t statistic when the null hypothesis is true?

**0**

A population has μ=50. What value of ó would make X=55 an extreme value out in the tail of the distribution?

**σ=1****z=x-μ/σ**

You have a score of X=65 on the exam. Which set of parameters would give you the best grade on the exam?

**μ=60 and σ=5**

Last week, Sarah had exams in math and in Spanish. On the math exam, the mean was μ=30 with a ó=5, and Sarah had a score of X=45. On the Spanish exam, the mean was μ=60 with a ó=8, and Sarah had a score of X=68. For

Which class should sara expect the better grade

**Math**

What is the position in the distribution corresponds to a z-score of z=-1.00?

**Below the mean by a distance equal to 1 standard deviation**

Which of the following z-score values represents the location farthest from the mean?

**z=-2.00**

For a population with μ=70 and σ=8, what is the z-score corresponding to x=82?

**+1.50****z=x-μ/σ**

For a population with a standard deviation of σ=10, what is the z-score corresponding to a score that is 5 points below the mean?

**Z = – 0.50**

For a population with μ=40 and σ=8, what is the z-score corresponding to x=34?

**– 0.75**

Under what circumstances can a very small treatment effect be statistically significant?

**If the sample size big and the sample variance is small**

Which of the following is a fundamental difference between the t statistic and a z-score?

**The t statistic uses the sample variance in place of the population variance.**

Which set of characteristics will produce the smallest value for the estimated standard error?

**A large sample size and a small sample variance**

A sample of n = 25 scores has a mean of M = 40 and a standard deviation of s = 10. What is the estimated standard error for the sample mean?

**2**

If other factors are held constant, what is the effect of increasing the sample size?

**It will decrease the estimated standard error and increase the likelihood of rejecting H0.**

If other factors are held constant, which set of sample characteristics is most likely to reject a null hypothesis stating that M = 80?

**M = 90 and small sample variance**

When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution?**It is flatter and more spread out than the normal distribution.**

A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df = 30, how many individuals were in the sample?

**n = 31**

With α = .01, the two-tailed critical region for a t test using a sample of n= 16 subjects would have boundaries of ______.

**t = ±2.947**

On average, what value is expected for the t statistic when the null hypothesis is true?

**0**