FM Qs Wrong

Question 1

Explain why it may be appropriate to carry out a hypothesis test based on the PMCC

Answer 1

Because scatter diagram illustrates a rough elliptical shape, so it suggests a bivariate normal distribution.

• also if there’s two big clusters

Question 2

Spearman’s hypothesis

Answer 2

H0 - there is no association between x and y
H1 - there is association between x and y

Question 3

Define significance level

Answer 3

The probability of rejecting the null hypothesis when it is in fact true

Question 4

Discuss briefly what the contingency excel table suggests

Answer 4

• go with each type, e.g:
  Type 1 - large contributions to test statistic of __ and __ show that fewer than expected are _ and more than expected are __
  Type 2 - for type 2, small contributions of ___, so as expected
  Type 3 - ….

Question 5

Interpolation vs extrapolation

Answer 5

Interpolation good estimate and reliable, extrapolation is probs unreliable

Question 6

Comment on the fit of the regression line

Answer 6

Because r^2 = ____, fit is bad/moderate/ good

And the points lie fairly far/close from the line of best fit

Question 7

Lil uniform distribution

Answer 7

Uniform on values {1,2,3….n}

Question 8

Much larger sample size =

Answer 8

Smaller critical value

Question 9

Residual =

Answer 9

Real - calculated

Question 10

Conditions for binomial (4)

Answer 10

• fixed number of observations
• each observation is independent
• each observation is either success or fail
• probability is constant

Question 11

Conditions to have position distribution

Answer 11

• all events independent of each other
• rate of events through time is constant (mean)
• mean = variance roughly

Question 12

Explain why for proper inference, PMCC sample should be randomly selected

Answer 12

Because then the probability basis on which the sample has been selected is known

Question 13

Conditions for geometric distribution

Answer 13

• independent trials
• binary - success or fail
• chance of success is the same each trial

Question 14

Degrees of freedom tips and tricks

Answer 14

1 - go from final tableau - after possibly merging columns due to small yute
2 - if testing for poisson binomial, you are estimating parameters, so v - 1, then -1 for the merged column

Question 15

Student concludes no correlation between variables in the summer months, ctm about the students conclusion

Answer 15

• result of hypothesis test always has uncertainty, and then expand related to that question

Question 16

Give two desirable features that the sample should have

Answer 16

• randomness
• unbiased
• representative of the population
• components selected independently

Question 17

Explain why random sample was chosen for PMCC

Answer 17

• random sample enables proper inference about population to be undertaken
• unbiased
• for hypothesis test to be valid, necessary to assume sample is random

Question 18

Explain why binomial and poission can be used

Answer 18

• occurrences are random and independent with constant probability
• number of successes are counted
  Therefore binomial appropriate

For poission, sample size is large, and p is small

Question 19

Sometimes when chatting about rough elliptical

Answer 19

• point out any anomalies too
• also mention POPULATION

Question 20

Reliability of regression estimate usually related to

Answer 20

EXTRAPOLATION OR INTERPOLATION
- sometimes slide in r value and points closeness to line too

Question 21

State the distributional assumption which is necessary for this test to be valid

Answer 21

The POPULATION
Must have a bivariate normal distribution

Question 22

Comment on the outcome of this test with a larger sample but with 0.076 being considered as an effect size

Answer 22

• test shows that there is/ isn’t almost certainly some real correlation in the population
• however this is of little practical consequence since effect size is so small

Question 23

Would it be appropriate to use regression y on to find a value of x given a venue of y

Answer 23

Not appropriate; the regression line of d on f is needed

Question 24

Based on weird effect size table + data, two reasons why it would not be appropriate to carry out a hypothesis test based on this data

Answer 24

• sample not random
• distribution of the bivariate population is unknown

Question 25

What does table + effect size allow u to conclude on the relationship between x and y

Answer 25

• point out largest effect size
• is it large or medium? Medium = less useful for practical purposes
• all other factors have low effect size, suggesting a very little relationship for them