Sampling

Question 1

Model

Answer 1

representation of a system, in some form other than that of the object itself

Question 2

Mean and standard Dev.

Answer 2

Sample mean= sum of all over population

The sample mean will always be in the sample but can be outside the population mean. Use just N we will be underestimating

st dev= (observed - mean)^2/ N
parameter

Sample
= /n - 1
statistic

n−1 is used in the denominator of the sample standard deviation formula to provide an unbiased estimate of the population variance and to account for the loss of a degree of freedom when estimating the sample mean.

Variance is squared bc don’t want things above the mean to cancel out below the mean and then sq rooted to revert to the og units

Question 3

Distribution

Answer 3

Divide the range of data into intervals
Label the x-axis according to chosen intervals
Find the frequency of occurrence in each interval
Label y-axis according to the frequency of occurrence
Plot!

Question 4

Goodness of Fit

Answer 4

Compare the histogram of observed data to the shape of the candidate distribution
Chi-squared etc.
Find the distribution with the best fit

Question 5

Chi Squared

Answer 5

Chi squared =
χ² = Σ [(O - E)² / E]

1. Formulate Hypotheses:
   
   • Null Hypothesis (H0): There is no significant relationship between gender and preferred smartphone brand.
2. Calculate Expected Frequencies: calculate the expected frequencies for each cell of the contingency table.
3. Compute Chi-Squared Statistic: Use the formula to calculate the chi-squared statistic.
4. Determine Degrees of Freedom: (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table
5. Find Critical Value or P-value: Look up the critical value for chi-squared distribution with 2 degrees of freedom at your chosen significance level (usually 0.05) or calculate the p-value using statistical software.
6. Make a Decision: If the calculated chi-squared value is greater than the critical value or the p-value is less than 0.05, reject the null hypothesis.

Question 6

Standard Error

Answer 6

σ / √n

Confidence interval +1.96 σ / √n

Question 7

Hypothesis Testing

Answer 7

Assume initial hypothesis is true
Calculate a plausible range of values
If sample is not in range, reject the hypothesis

Question 8

T-Stat Hypothesis Testing

Answer 8

How many standard errors the value is from the null hypothesis for the mean

test stat - mean / standard error

> 1.96 then reject

Question 9

Comparison of Samples

Answer 9

H0: mean - mean = 0 (test stat)

Approach: – measure the difference between the means of each group – calculate st. error for this statistic – perform a hypothesis test

St. Error = (st. error^2 + st. error)
root

Question 10

Parameter Vs Statistic

Answer 10

Parameter: fixed value calculated from every individual in the population

Stat: Calculated from only some of the populayion