Confidence Intervals

Question 1

Point Estimate

Answer 1

• uses a single value to estimate a population parameter
• doesnt express the uncertainty

Question 2

Interval estimate

Answer 2

• uses a range of values to estimate a population parameter.
• Confidence Interval

Question 3

What’s the equation for Confidence Interval?

Answer 3

= sample statistic (mean) ± margin of error

Question 4

Main Components of Confidence Interval

Answer 4

• sample statistic
• margin of error
• confidence level

Question 5

Sample Statistic

Answer 5

sample mean or sample proportion

Question 6

Confidence level

Answer 6

• The confidence level describes the likelihood that a particular sampling method will produce a confidence interval that includes the population parameter.
• common confidence levels
  
  • 90%
  • 95% - most popular
  • 99%

Question 7

margin of error

Answer 7

ME = z-score * SE (large smaple n>=30)
ME = t-score * SE (small sample n<30)

represents the maximum expected difference between a population parameter and a sample estimate.
- This range of values expresses the uncertainty in your estimate due to random sampling

Question 8

Steps to Construct Confidence Interval

Answer 8

1. Identify a sample statistic.
2. Choose a confidence level.
3. Find the margin of error.
4. Calculate the interval.

Question 9

Why does data professional use confidence interval?

Answer 9

to help describe the uncertainty surrounding an estimate.

Question 10

Interpretation of the confidence interval

Answer 10

Technically, 95% confidence means that if you take repeated random samples from a population, and construct a confidence interval for each sample using the same method, you can expect that 95% of these intervals will capture the population mean. You can also expect that 5% of the total will not capture the population mean.

Question 11

Incorrect interpretation of the confidence interval

Answer 11

1. 95% refers to the probability that the population mean falls within the constructed interval. It’s not correct to say there is a 95% chance that your confidence interval captures the population mean because this implies that the population mean is variable. Intervals change from sample to sample, but the value of the population mean is constant
2. 95% refers to the percentage of data values that fall within the interval
3. 95% refers to the percentage of sample means that fall within the interval

Question 12

Z-scores

Answer 12

For large sample sizes, you use z-scores to calculate the margin of error.
This is because of the central limit theorem: for large sample sizes, the sample mean is approximately normally distributed.

For a standard normal distribution, also called amz-distribution, you usez-scores to make calculations about your data.

Question 13

T-scores

Answer 13

For small sample sizes (n < 30), you need to use the t-distribution.

Statistically speaking, this is because there is more uncertainty involved in estimating the standard error for small sample sizes

But, the t-distribution has bigger tails than the standard normal distribution does. The bigger tails indicate the more outliers that come with a small dataset.

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

When the sample size = 30, the distributions are practically the same, and you can use z-score for your calculations.

Question 14

CI Step 1: Identify a sample statistic

Answer 14

IF your sample represents the average emissions rate for 15 engines. You’re working with a sample mean.

Question 15

CI Step 2: Choose a confidence level

Answer 15

common confidence levels
- 90%
- 95% ( most popular)
- 99%

Question 16

CI Step 3: Find the margin of error

Answer 16

large sample size n ≥ 30
ME = z-score * SE

small sample n < 30
ME = t-score * SE

Question 17

Standard Error for sample mean

Answer 17

SE = S/√n

S = std

Question 18

Standard Error for sample proportion

Answer 18

SE = √ [p (1-p) / n)]

Question 19

degree of freedom

Answer 19

The t-distribution is defined by a parameter called the degree of freedom.

dof = sample size - 1

Question 20

CI Step 4: Calculate the interval

Answer 20

sample statistic (mean/proportion) ± margin of error

for mean [12,30]
for proportion [14%, 20%]

Question 21

Relationship between confidence level and confidence interval

Answer 21

the confidencelevelgets higher, the confidenceintervalgets wider.