NORMAL DISTRIBUTION AND CONFIDENCE INTERVALS

Question 1

What is the relationship between standard deviation and variance?

Answer 1

Variance is the square of standard deviation

Question 2

What does the a% point signify?

Answer 2

The 𝛼% percentage point gives the range of values of the standard normal distribution which excludes 𝛼% of the population

Question 3

What does the confidence interval do?

Answer 3

The confidence interval gives a range of values for the population parameter being measured (indirectly through the sample statistic)

Question 4

What does a B% confidence interval tell us

Answer 4

𝛽% of the time the confidence interval contains the population mean. 𝛽 is the confidence level.

Question 5

What is the difference between confidence interval estimation for small and large sample sizes?

Answer 5

For small samples (rule of thumb n<60) the sample SD 𝑠 is not an accurate estimate of the population SD 𝜎.

We need to allow for this extra uncertainty in our calculation of the confidence interval.

Solution: use a percentage point of a t-distribution, instead of the normal distribution

Replace z with t in the formular

x +/- z x SE

Small sample
x +/- t x SE

Question 6

What is degree of freedom?

Answer 6

The maximum number of independent values that are allowed to vary in a sample without breaking any constraints

Question 7

Explain a myth about confidence intervals

Answer 7

People think confidence intervals are fixed and the true value may end up in the interval, the reverse is the case, as true values are fixed and the interval may end up around it

Question 8

What does the central limit theorem state?

Answer 8

The central limit theorem says that the sample means are approximately normally distributed, even if the population distribution is non-normal.

The approximation is closer for larger samples.

Question 9

What is bootstrapping?

Answer 9

Bootstrapping is a statistical procedure that resamples a single dataset to create many simulated samples. This process allows you to calculate standard errors, construct confidence intervals, and perform hypothesis testing for numerous types of sample statistics. It is a method that aids in calculating confidence intervals for a small sample size

Question 10

What is a logarithm?

Answer 10

In its simplest form, a logarithm answers the question: How many of one number multiply together to make another number?

That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 103, the logarithm base
10
{\displaystyle 10} of 1000 is 3, or log10 (1000) = 3.