# Sample Variance & Small Sample Size – Statistics

### 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?

##### 85x = 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

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