7: Hypothesis Testing

Question 1

What does the symbol ‘H0’ represent?

(subscript zero)

Answer 1

H0 is the null hypothesis, a speculated assumption or a statement to be tested.

Question 2

What does the symbol ‘H1’ represent?

(subscript 1)

Answer 2

H1 is the alternative hypothesis, the exact opposite of the null hypothesis.

Question 3

Based on a statistical investigation, what are the two possible outcomes of hypothesis testing?

Answer 3

Reject H0 and adopt H1

OR

Conclude that there is no evidence to reject H0

Question 4

What is a type 1 error?

Answer 4

We reject the null hypothesis when it is true

Question 5

What is a type 2 error?

Answer 5

The null hypothesis is not rejected when it is false

Question 6

What is the significance level?

Answer 6

The probability ‘alpha’ of making a type 1 error

Question 7

What is the process for the one sample z-test for population mean? (7 steps)

Answer 7

1 - Define null hypothesis (H0)
2 - Define alternative hypothesis (H1)
3 - Define significance level (normally 1 or 5%)
4 - Determine rejection region using z-table
5 - Calculate the value of the test statistic (z)
6 - Compare test statistic to rejection region
7 - Formulate written conclusion

Question 8

How is the written conclusion normally formatted if the test statistic falls within the rejection region?

Answer 8

The null hypothesis is rejected and the alternative hypothesis is adopted. There is evidence to suggest a significant difference between the sample mean and the hypothesised population mean.

Question 9

what is ‘x squiggly line’?

Answer 9

Sample mean

Question 10

What is ‘mu 0’?

Answer 10

Assessed population mean, comes from H0

Question 11

what is ‘sigma’?

Answer 11

Known or previously estimated population standard deviation

Question 12

What is ‘n’?

Answer 12

Sample size

Question 13

How would you formulate the null hypothesis (H0) for the below scenario?

What would the formula be?

‘A local authority has introduced a car sharing scheme and has provided car parking data for the last two years prior to the scheme, and for 75 days subsequent to implementing the scheme.’

Answer 13

H0 = the average number of cars remains the same or has not decreased. In other words, the scheme does not work.

Sigma = Sigma 0 (i.e. no change)

Question 14

How would you formulate the alternative hypothesis (H1) for the below scenario?

What would the formula be?

‘A local authority has introduced a car sharing scheme and has provided car parking data for the last two years prior to the scheme, and for 75 days subsequent to implementing the scheme.’

Answer 14

H1 = the average number of cars, population mean, has decreased. In other words, the scheme does work.

Sigma < Sigma 0 (i.e. population mean has decreased)

Question 15

How do you convert the significance level (alpha) from % to decimal?

Answer 15

Divide by 100

Question 16

What are the three forms of hypothesis testing and the equivalent formulas?

Answer 16

two-tailed test: sigma ≠ sigma 0 (not equal to)

left-tailed test: sigma < sigma 0 (less than)

right-tailed test: sigma > sigma 0 (greater than)

Question 17

Where is the rejection area for the two-tailed test?

How is alpha converted?

Answer 17

At both the left and rightmost extents.

alpha/2, it is negative on the left and positive on the right.

Question 18

Where is the rejection area for the left-tailed test?

How is alpha converted?

Answer 18

At the leftmost extent.

Alpha is negative.

Question 19

Where is the rejection area for the right-tailed test?

How is alpha converted?

Answer 19

At the rightmost extent.

Alpha is positive.

Question 20

How do you find the corresponding Z value on the Z table?

Answer 20

1 - Significance level (decimal), then find the value in the body of the table and read off the corresponding row and column values.

Question 21

How do you find the corresponding Z value if the number is between two columns?

For example, 1.64 and 1.65

Answer 21

Add both columns together and divide by 2 (average them).

(1.64+1.65/2)=1.645

Question 22

Propose a conclusion to the following scenario:

The test statistic, Z, has fallen within the rejection region for the below:
H0 - Car sharing scheme has not worked
H1 - Car sharing scheme has worked
5% occurrence

Answer 22

The alternative hypothesis is adopted: there is significant statistical evidence that the population mean (average number of parked cars per day) has reduced, because the sample mean falls within the region associated with just 5% occurrence.

Question 23

What formula do you use for hypothesis testing for a significant difference between two sample means?

Answer 23

The ‘Z calc’ formula

Question 24

What are the two hypothesis options for two sample mean hypothesis testing?

Answer 24

H0: (sigma 1 - sigma 2) = 0 (no significant diff.)

H1: (sigma 1 - sigma 2) ≠ 0 (significant diff.)

Question 25

In hypothesis testing with two sample means, what do the subscripts 1 and 2 refer to?

Answer 25

1 relates to the first sample and it’s assumed population and 2 relates to the second sample and it’s assumed population.

Question 26

What type of test are two sample means tests typically?

Answer 26

Two-tailed tests

Question 27

What is the rejection region for a two-tailed test?

Answer 27

• Z value < x > + Z value

Question 28

If no data exists for sigma 1 and/or sigma 2 (population standard deviation) what formula must be used to estimate this?

Answer 28

sigma est 1 = s1 * Sqr Root (n1/n1-1)

and the same for 2 with the second population values in place.

Question 29

How do you phrase the acceptance of the null hypothesis in a multi population mean question?

Answer 29

There is not sufficient evidence to suggest the two samples have come from different populations, so the conclusion is that they come from the same population.

Question 30

How do you phrase the rejection of the null hypothesis in a multi population mean question?

Answer 30

There is significant evidence to suggest that the samples have come from different populations.