Formative 4.2: T-Distribution

Front

What is the t-distribution used for?

Back

The t-distribution is used with small samples taken from populations that are approximately normal.

Front

What is the formula for degrees of freedom (df) in a sample?

Back

df = n - 1, where n is the sample size.

Front

If a two-tailed graph of the t-distribution has a df = 28 and the non-shaded area is 90%, what is the margin of error?

Back

0.10

Front

What is the critical value for a t-distribution with df = 23 at a 95% confidence level?

Back

2.069

Front

Find the degree of freedom for a sample size of n = 15.

Back

df = 14.

Front

What does a higher degree of freedom indicate in a t-distribution?

Back

A higher degree of freedom indicates a closer approximation to the normal distribution.

Front

What is the relationship between sample size and degrees of freedom?

Back

As the sample size increases, the degrees of freedom also increase.

Front

What is the significance of the t-distribution in hypothesis testing?

Back

The t-distribution is significant in hypothesis testing for small sample sizes, providing a more accurate estimate of the population parameter.

Front

How does the t-distribution differ from the z-distribution?

Back

The t-distribution is used for smaller sample sizes and has heavier tails than the z-distribution, which is used for larger samples.

Front

What is the effect of sample size on the shape of the t-distribution?

Back

As the sample size increases, the t-distribution approaches the shape of the normal distribution.