BA 2 - Sampling and Estimation

Question 1

What type of sample ensures sound inferences?

Answer 1

• Sufficiently large; and

- Representative of the population

Question 2

How to avoid biased results

Answer 2

• Phrasing questions neutrally
• Ensuring that the sampling method is appropriate for the demographic of the target population; and
• Pursuing high response rates.

Question 3

Characteristics of the normal distribution

Answer 3

• Symmetrical bell shape;
• Center => mean, width => standard deviation;
• ~68% of the probability contained within 1 sd of mean, ~95% within 2 sds, ~99.7% within 3 sds.

Question 4

z-value

Answer 4

Normalized value.

z = (x - mu)/sd

Question 5

Central Limit Theorem

Answer 5

if we take enough sufficiently large samples from any population, the means of those samples will be normally distributed, regardless of the shape of the underlying population.

Question 6

Distribution of Sample Means

Answer 6

• Approximates normal curve as we increase the number of samples;
• Mean of any sample lies within this curve - we can use the properties of the normal curve to draw conclusions about the sample;
• mean of this distribution = mean of the population distribution;
• sd of this distribution = (sd of population)/rt. n;
• => increasing sample size decreases the width of the distribution of sample means.

Question 7

Confidence Interval

Answer 7

Range around the sample mean to estimate the range in which the true population mean likely lies.

• Width depends on level of confidence, estimate of population sd, sample size.

Question 8

Size of sample

Answer 8

Large samples => greater than or equal to thirty.
Small sample => t-distribution - shorter, wider than normal distribution.
Large => normal distribution

Question 9

Confidence intervals for proportions

Answer 9

Need to create a dummy (0, 1) variable.

And then proceed as we would with any other variable.

Question 10

Ensuring sample size is large enough for estimating population proportion

Answer 10

n.p >= 5, and

n(1-pbar) >=5

Question 11

[EXCEL] Generating random number between 0 and 999

Answer 11

=RAND()

Question 12

[EXCEL] Cumulative probability for normal distribution

Answer 12

=NORM.DIST(x, mean, sd, cumulative)

cumulative = TRUE

Question 13

[EXCEL] Cumulative probability for standardized normal distribution

Answer 13

=NORM.S.DIST(z, cumulative)

cumulative = TRUE

Question 14

[EXCEL] Corresponding x-value for probability on a specified normal distribution

Answer 14

=NORM.INV(probability, mean, sd)

Question 15

[EXCEL] Margin of error for normal distribution

Answer 15

=CONFIDENCE.NORM(alpha, sd, sample_size)

For sample size greater than or equal to 30

Question 16

[EXCEL] Margin of error for t distribution

Answer 16

=CONFIDENCE.T(alpha, sd, sample_size)

For sample size less than 30

Question 17

[EXCEL] Creating conditional subset

Answer 17

=IF(logical_test, [value_if_true], [value_if_false])