1 & 2 tailed hypothesis testing

Question 1

What is a 1 tailed hypothesis?

Answer 1

A hypothesis that seems to lead to one direction (directional)

Question 2

Our sample mean maths scores will be higher than the maths scores of the general UK population

Is this a 1-tailed or 2-tailed hypothesis?

Answer 2

1-tailed hypothesis (right-hand tail)

Question 3

What are the 2 types of 1-tailed hypotheses?

Answer 3

1) 1-tailed right hand tail
2) 1-tailed left hand tail

Question 4

What is a 1-tailed right-hand hypothesis?

Answer 4

• A hypothesis that only leads to one direction
• A hypothesis that leads to a direction suggesting that the sample mean is BETTER THAN or HIGHER THAN the population mean

Question 5

Our sample mean maths scores will be lower than the maths scores of the general UK population

Is this a 1-tailed or 2-tailed hypothesis?

Answer 5

1-tailed hypothesis (left-hand tail)

Question 6

What is a 1-tailed left-hand hypothesis?

Answer 6

• A hypothesis that only leads to one direction
• A hypothesis that leads to a direction suggesting that the sample mean is WORSE THAN or LOWER THAN the population mean

Question 7

What is a 2-tailed hypothesis?

Answer 7

A non-directional hypothesis that doesn’t commit to a particular direction of effects

Question 8

There will be a difference in our sample’s mean maths scores and the UK population’s mean maths scores

Is this a 1-tailed or 2-tailed hypothesis?

Answer 8

2-tailed hypothesis

Question 9

How do you evaluate the inconsistency of a 2-tailed hypothesis with the H0?

Answer 9

We must work out the area under the SND on both ends (HIGHER/BETTER THAN and LOWER/WORSE THAN the pop. mean)

1) Find z score
2) Find p-value on the table using the z score
3) Because the area under SND of the 2 tails are the same, we basically just double the p value
4) The doubled p-value = probability of our sample mean being DIFFERENT to the pop. mean

Question 10

How do you decide whether to form a 1-tailed or 2-tailed hypothesis?

Answer 10

1-tailed = When you have a good reason to be able to predict that the effect should be in a particular direction

e.g. Measuring if people who drink alcohol could walk in a straight line (based on previous studies, we know they can’t)

2-tailed = If you can’t determine an effect in a particular direction

Question 11

An alien hires you to test his hypothesis that the 25 members of his elite Ziltoidian Special Advisory Group (Z-SAG) are significantly shorter than the mean height in the population.

True or False: President Zdave’s hypothesis is 2-tailed

a. True
b. False

Answer 11

False

It’s a left-hand 1-tailed hypothesis

Question 12

Visiting aliens from Ziltoidia 10 are rather self-conscious about their height. As a population, their height in cm follows a normal distribution: N(25, 2.5). In particular, President Zdave (the Ziltoidian commander-in-chief) is keen to appear taller and is confident that his group of advisors help him in this regard since he thinks he is about average height for the population whereas he suspects several of his advisors are smaller than the population mean. He hires you to test his hypothesis that the 25 members of his elite Ziltoidian Special Advisory Group (Z-SAG) are significantly shorter than the mean height in the population.

After collecting the height data you discover that the sample mean height for Z-SAG is 24.5.

What is the most appropriate report to send President ZDave based on the outcome of a z-test of his hypothesis?

a.	z = -1, p = 0.1587 Since p > 0.05 President Zdave can not reject his null hypothesis - ZSAG members are not atypically short on average compared to samples of the same size from the population.

b.	z = -0.2, p = 0.4207 Since p > 0.05 President Zdave can not reject his null hypothesis - ZSAG members are not atypically short on average compared to samples of the same size from the population.

c.	z = -5, p = 0.0000 Since p < 0.05 President Zdave can reject his null hypothesis - ZSAG members are atypically short on average compared to samples of the same size from the population.

d.	z = -1, p = 0.8413 Since p > 0.05 President Zdave can not reject his null hypothesis - ZSAG members are not atypically short on average compared to samples of the same size from the population.

Answer 12

e.s.e. = pop SD / SQRT (sample size)
e.s.e. = 2.5 / SQRT (25)
e.s.e. = 0.50

z score = (x - mean) / e.s.e.
z score = (24.5 - 25) / 0.50

z score = -1
p value = 0.1587
p > 0.05, fail to reject null hypothesis

Answer = A

Question 13

You formulate a research hypothesis that average minutes spent sleeping per night for Ziltoidians on earth will be different to the equivalent figure on Ziltoidia 10. You then collect sleep data for a random sample of 36 Ziltoidians on earth, measuring (to the nearest minute) how long they sleep per night and find the sample mean is 326 minutes.

True or false - your research hypothesis is 1-tailed

a. True
b. False

Answer 13

False (it is 2-tailed)

Question 14

Visiting aliens form Ziltoidia 10 are used to different levels of daylight, since they come from a differnt solar system and their planet has a different orbit around their sun. President Zdave is interested in the effects of earth daylight on Ziltoidian sleeping habits. He knows that on Ziltoidia 10 minutes spent sleeeping per night follows a normal distribution: N(312, 48). He comes to you to ask you to run an experiment to test whether Ziltoidian sleeping times differ on earth.

You then collect sleep data for a random sample of 36 Ziltoidians on earth, measuring (to the nearest minute) how long they sleep per night and find the sample mean is 326 minutes.

What is the most appropriate report to send President ZDave based on the outcome of a z-test of this hypothesis?

a.  z = 0.2917, p = 0.7706 Since p > 0.05 we can not reject the null hypothesis that average minutes spent sleeping per night for Ziltoidians on earth is no different to the equivalent figure on Ziltoidia 10.

 

b.  z = 1.75, p = 0.0401 Since p < 0.05 we can reject the null hypothesis in favour of the research hypothesis that average minutes spent sleeping per night for Ziltoidians on earth is different to the equivalent figure on Ziltoidia 10.

c.  z = 1.75, p = 0.0802 Since p > 0.05 we can not reject the null hypothesis that average minutes spent sleeping per night for Ziltoidians on earth is no different to the equivalent figure on Ziltoidia 10.

d.  z = 0.2917, p = 0.3853 Since p > 0.05 we can not reject the null hypothesis that average minutes spent sleeping per night for Ziltoidians on earth is no different to the equivalent figure on Ziltoidia 10.

Answer 14

e.s.e. = pop SD / SQRT (sample size)
e.s.e. = 48 / SQRT (36)
e.s.e. = 8.00

z score = (x - mean) / e.s.e.
z score = (326 - 312) / 8.00

z score = 1.75
p value = 0.0802
p > 0.05, fail to reject null hypothesis

Answer = C