Lesson test: Counts and categories

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Counts and categories

1.[2p]
Mendel observed 5474 round and 1850 wrinkled seeds out of 7324, against a 3 to 1 prediction. What is the expected number of round seeds?

CorrectNot quite: 5493

2.[3p]
A die is rolled 600 times giving 95, 102, 108, 96, 110 and 89. What is $X^{2}$ , to one decimal place?

CorrectNot quite: 3.3

3.[3p]
How many degrees of freedom does a goodness-of-fit test have?

The number of categories, less one, less the number of parameters estimated from the data

Correct

The number of categories

The answer is: The number of categories, less one, less the number of parameters estimated from the data

The sample size less one

The answer is: The number of categories, less one, less the number of parameters estimated from the data

The number of categories less the sample size

The answer is: The number of categories, less one, less the number of parameters estimated from the data

4.[2p]
How many degrees of freedom does a chi-squared test of independence have for a 4 by 3 table?

CorrectNot quite: 6

5.[2p]
In a two-way table, why is the expected count $R_{i} C_{j} / n$ ?

Independence makes the cell probability the product of the marginal probabilities, estimated from the margins

Correct

It is the average of the row and column totals

The answer is: Independence makes the cell probability the product of the marginal probabilities, estimated from the margins

It makes every expected count equal

The answer is: Independence makes the cell probability the product of the marginal probabilities, estimated from the margins

It is required for the counts to sum to $n$

The answer is: Independence makes the cell probability the product of the marginal probabilities, estimated from the margins

6.[2p]
The rule that counts should be at least 5 applies to the observed counts, not the expected ones.

True

The answer is: False

False

Correct

7.[3p]
The Salk trial gives a pooled two-proportion $z$ of 6.727. What is the corresponding $X^{2}$ for the 2 by 2 table, to one decimal place?

CorrectNot quite: 45.3

8.[3p]
Why did Fisher regard Mendel's combined $X^{2}$ of 41.6 on 84 degrees of freedom as a problem?

Select all that apply

The expected value of $X^{2}$ is the degrees of freedom, so 41.6 is far too small

Correct

A fit that close has probability about 0.00003 under honest sampling

Correct

A test can be failed from the too-good side as well as the too-bad side

Correct

A small $X^{2}$ proves the genetic model is wrong

The answer is: The expected value of $X^2$ is the degrees of freedom, so 41.6 is far too small, A fit that close has probability about 0.00003 under honest sampling, A test can be failed from the too-good side as well as the too-bad side

9.[3p]
Match each situation to the right response.

Expected counts below 5
A significant table with many cells
A significant result in a huge table
A significant association

inspect the residuals
use Fisher's exact test
report an association measure
no causal claim is licensed

Show the answer

Expected counts below 5: use Fisher's exact test A significant table with many cells: inspect the residuals A significant result in a huge table: report an association measure A significant association: no causal claim is licensed

1.[2p] Mendel observed 5474 round and 1850 wrinkled seeds out of 7324, against a 3 to 1 prediction. What is the expected number of round seeds?

2.[3p] A die is rolled 600 times giving 95, 102, 108, 96, 110 and 89. What is X2, to one decimal place?

3.[3p] How many degrees of freedom does a goodness-of-fit test have?

4.[2p] How many degrees of freedom does a chi-squared test of independence have for a 4 by 3 table?

5.[2p] In a two-way table, why is the expected count RiCj/n?

6.[2p] The rule that counts should be at least 5 applies to the observed counts, not the expected ones.

7.[3p] The Salk trial gives a pooled two-proportion z of 6.727. What is the corresponding X2 for the 2 by 2 table, to one decimal place?

8.[3p] Why did Fisher regard Mendel's combined X2 of 41.6 on 84 degrees of freedom as a problem?

9.[3p] Match each situation to the right response.

1.[2p]
Mendel observed 5474 round and 1850 wrinkled seeds out of 7324, against a 3 to 1 prediction. What is the expected number of round seeds?

2.[3p]
A die is rolled 600 times giving 95, 102, 108, 96, 110 and 89. What is $X^{2}$ , to one decimal place?

3.[3p]
How many degrees of freedom does a goodness-of-fit test have?

4.[2p]
How many degrees of freedom does a chi-squared test of independence have for a 4 by 3 table?

5.[2p]
In a two-way table, why is the expected count $R_{i} C_{j} / n$ ?

6.[2p]
The rule that counts should be at least 5 applies to the observed counts, not the expected ones.

7.[3p]
The Salk trial gives a pooled two-proportion $z$ of 6.727. What is the corresponding $X^{2}$ for the 2 by 2 table, to one decimal place?

8.[3p]
Why did Fisher regard Mendel's combined $X^{2}$ of 41.6 on 84 degrees of freedom as a problem?

9.[3p]
Match each situation to the right response.