Sample distribution; standard error; confidence interval; Using confidence intervals

Question 1

What are population parameters?

Answer 1

μ = population mean.
σ^2 = population variance.
σ = population standard deviation.

Question 2

What are sample statistics?

Answer 2

The mean (M), variance (S^2), and standard deviation of a sample (SD/ S)

Question 3

How can we learn about populations?

Answer 3

By using sample for inference about population

Question 4

What is a disadvantage of samples?

Answer 4

Sample does not give true picture. It’s like seeing the

world through frosted glass.

Question 5

how is the accuracy of samples affected?

Answer 5

• Multiple samples of same size (N) differ in their means
  (even though all from same population).

-When we take infinitely many sample means we get
the sample distribution.

• Sample distribution is sometimes wide and sometimes narrow.

Question 6

What forms a sample distribution?

Answer 6

multiple sample means form a distribution.

Question 7

What is an advantage of narrower ditributions?

Answer 7

They are more sensible and offer greater trust

Question 8

What forms a narrow distribution?

Answer 8

• Larger N (number of means) = narrower sample distribution.
  (Law of Large Numbers).
• Lower σ (population standard deviation) = narrower sample distribution.
  (If σ = 0, every sample mean will be spot on)

Question 9

What is a standard error (SE)?

Answer 9

The Standard Deviation of the Sample distribution

Question 10

What does Standard Error (SE) represent?

Answer 10

SE reflects how far, on average, M (mean) is off the mark as an estimate of μ (population mean).

Question 11

How to describe width of sample distribution?

Answer 11

Narrow sample distribution = M is trustworthy.

Question 12

How do you calculate SE?

Answer 12

σ
SE = ——-
√N

Question 13

What is the shape of sampling distributions and what is it based on?

Answer 13

Sampling distribution also has symmetric shape and is centred around μ.

Question 14

How can you find σ (population standard deviation) to calculate Standard Error?

Answer 14

SD to estimate σ

Thus, we estimate SE as . SD/ √N

Question 15

How can we increase the precision of our estimate?

Answer 15

To increase the precision of our estimate we can increase N (number of means).

Question 16

What is the range of plausible values?

Answer 16

Which number seems more plausible from the point estimate calculated

Question 17

What is the 95% Confidence Interval?

Answer 17

(CI) is a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed as a % whereby a population mean lies between an upper and lower interval.

Question 18

How do you calculate CI?

Answer 18

because 95% of score lie between the interval of -1.96 SD and +1.96 SD:

M -1.96 x SE
M +1.96 x SE

Question 19

How is CI reported in a research report?

Answer 19

CI is reported in square brackets after the mean:
M = 15, 95% CI [13.04, 16.96].
After Cohen’s d

Question 20

Why is CI important?

Answer 20

Confidence intervals (CIs) are the best way to capture the inaccuracy in sample results.