Module 3 Hypothesis Testing

Question 1

What is the null hypothesis (Ho)?

Answer 1

A statement about a topic of interest regarding the population, typically based on historical information or conventional wisdom.

The null hypothesis is the opposite of the alternative hypothesis.

Question 2

What is the alternative hypothesis (H1)?

Answer 2

The theory or claim we are trying to substantiate.

It is what we aim to prove through hypothesis testing.

Question 3

What is the first step in conducting a hypothesis test?

Answer 3

State the null and alternative hypotheses.

This sets the foundation for the test.

Question 4

What should be determined before conducting a hypothesis test?

Answer 4

Analyze a change in a single population or compare two populations, and decide on a one-sided or two-sided hypothesis test.

This influences the approach and analysis of the hypothesis test.

Question 5

What is the p-value?

Answer 5

The likelihood of obtaining a sample as extreme as the one obtained if the null hypothesis is true.

It helps in determining the strength of the evidence against the null hypothesis.

Question 6

How does the p-value of a one-sided hypothesis test compare to that of a two-sided test?

Answer 6

The p-value of a one-sided hypothesis test is half the p-value of a two-sided hypothesis test.

This is due to the nature of testing in one direction versus two directions.

Question 7

Explain what happens if the sample mean falls in the range of likely sample means?

Answer 7

When we’re developing a hypothesis, we can construct a range around the historical mean for that population; if the mean has NOT changed, it would be very likely that the sample mean falls within that range (remember the example of the movie theatre owner).

So, if it does, then we do not have sufficient evidence to reject the null hypothesis.

This indicates that the sample is consistent with the null hypothesis.

Question 8

What indicates sufficient evidence to reject the null hypothesis?

Answer 8

If the sample mean falls in the rejection region or if its p-value is lower than the stated significance level.

Rejecting the null hypothesis suggests the alternative hypothesis may be true.

Question 9

True or False: We can accept the null hypothesis.

Answer 9

False.

We can only fail to reject the null hypothesis.

Question 10

What is the significance level in hypothesis testing?

Answer 10

The threshold at which we decide whether to reject the null hypothesis. It represents the probability of rejecting the null hypothesis when it is true. It is denoted as alpha.
For example, a significance level of alpha = 0.05 means there is a 5% chance of rejecting the null hypothesis when it is true.

Common significance levels are 0.05, 0.01, and 0.10.

Question 11

Fill in the blank: The null hypothesis is tested by gathering data from a _______.

Answer 11

sample or samples.

Question 12

What is the null hypothesis denoted as?

Answer 12

The null hypothesis is denoted as H0.

Question 13

What does it mean to reject the null hypothesis?

Answer 13

To reject the null hypothesis means to conclude that there is sufficient evidence to support the alternative hypothesis.

Question 14

What does it mean to not reject the null hypothesis?

Answer 14

Not rejecting the null hypothesis means there is insufficient evidence to support the alternative hypothesis.

Question 15

What is the relationship between confidence level and type I error?

Answer 15

The higher the confidence level, the lower the chance of rejecting the null hypothesis when it is true (type I error or false positive).

Question 16

What is the relationship between confidence level and type II error?

Answer 16

The higher the confidence level, the higher the chance of not rejecting the null hypothesis when it is false (type II error or false negative).

Question 17

What is a type I error?

Answer 17

A type I error occurs when the null hypothesis is true, but we reject it.

This has a 5% chance of occurring at a 95% confidence level.

Question 18

What is a type II error?

Answer 18

A type II error occurs when the null hypothesis is false, but we fail to reject it.

Question 19

What is the correct conclusion when the null hypothesis is true?

Answer 19

The correct conclusion is to fail to reject the null hypothesis, which has a 95% chance of occurring.

Question 20

What is the correct conclusion when the null hypothesis is false?

Answer 20

The correct conclusion is to reject the null hypothesis.

Question 21

What function is used to calculate the p-value associated with a t-test?

Answer 21

The function used is T.TEST(array1, array2, tails, type).

Question 22

What does array1 represent in the T.TEST function?

Answer 22

Array1 is a set of numerical values or cell references.

Question 23

What does array2 represent in the T.TEST function?

Answer 23

Array2 is a set of numerical values or cell references. If only one set of data is available, the second data set should be a column with every entry as the historical mean.

Question 24

What does the ‘tails’ parameter specify in the T.TEST function?

Answer 24

The ‘tails’ parameter specifies the number of tails for the distribution. It should be set to 1 for a one-sided test or 2 for a two-sided test.

Question 25

What are the possible values for the ‘type’ parameter in the T.TEST function?

Answer 25

The ‘type’ parameter can be 1, 2, or 3.

Question 26

What does Type 1 indicate in the T.TEST function?

Answer 26

Type 1 is a paired test used when the same group is tested twice to provide paired ‘before and after’ data for each member of the group.

Question 27

What does Type 2 indicate in the T.TEST function?

Answer 27

Type 2 is an unpaired test in which the samples are assumed to have equal variances.

Question 28

What does Type 3 indicate in the T.TEST function?

Answer 28

Type 3 is an unpaired test in which the samples are assumed to have unequal variances. Typically, Type 3 is used unless there is a good reason to believe two samples have equal variances.

Question 29

What does the excel function CONFIDENCE.NORM do?

Answer 29

It returns the confidence interval for a population mean, using a normal distribution.

Question 30

Fill in the blank: The CONFIDENCE.NORM function is used when the sample size is ______.

Answer 30

large

Question 31

What is the syntax of the CONFIDENCE.NORM function?

Answer 31

CONFIDENCE.NORM(alpha, standard_dev, size)

Question 32

What is the confidence interval showing in this data, if the sample mean is 30?
0.05 Significance level (alpha)
2.5 standard deviation
50 sample size
Result 0.692952

Answer 32

Confidence interval is +/- 0.692952. So we can be 95% confident the true mean of the population is within that interval of the sample mean

Question 33

What is the difference between a one-sided and two-sided hypothesis test

Answer 33

A one-sided test specifies a particular direction of effect e.g. traffic to a website increasing after a design change. A two-sided test allows the change to be in either direction.

Question 34

What is a 95% range of likely sample means?

Answer 34

The range of likely sample means is used to help understand how likely it would be to get a sample mean different from the population mean, if the population mean is unchanged.
So with a 95% range of likely means, that means that if the population mean is still e.g. 6.7, 95% of all samples drawn from the population will have averages (means) that fall within that range