Business 212: Business Statistics Ch 11. Hypothesis Testing in Business

hypothesis test

• the formal procedures that statisticians use to test whether a hypothesis can be accepted or not

• an assumption about something

null hypothesis

the hypothesis based on chance

alternate hypothesis

the hypothesis that shows a change from the null hypothesis that is caused by something

P-value

less than the significance level, then the null hypothesis is not valid

region of acceptance

a chosen range of values that results in the null hypothesis being stated as valid

significance level

the probability of making the mistake of saying that the null hypothesis is not valid when it actually is true

What is the first step in a hypothesis test?

1. Creating an analysis plan

2. Interpreting the results

3. Publishing your findings

4. Writing the hypothesis

5. Analyzing the data

Writing the hypothesis

If the region of acceptance for a certain hypothesis is from 0% to 5%, then which of the following results is within the region of acceptance?

1. 80%

2. 1%

3. 99%

4. 100%

5. 35%

1%

What is a hypothesis?

1. A true statement.

2. A false statement.

3. An assumption about something.

4. The probability that something is true.

5. An assumption about probability.

An assumption about something.

A scientist is testing the growth speeds of a species of algae, and makes the following null hypothesis: Specimens of this species grow at a rate of at least v. They set their region of acceptance at 95% or higher, and find that 93% of the specimens grow at a rate of at least v. What should the scientist do and why?

1. They should accept the null hypothesis, because their results are outside of the region of acceptance.

2. They shouldn't perform the experiment again, because their results are outside of the region of acceptance.

3. They should reject the null hypothesis, because their results are outside of the region of acceptance.

4. They should perform the experiment again, because their results are outside of the region of acceptance.

They should reject the null hypothesis, because their results are outside of the region of acceptance.

How many hypotheses do you write in a hypothesis test?

1. 3

2. 1

3. 2

4. 0

5. 4

2

standard deviation

• the amount of variation in a set of data values

• the variability of individual observations around their mean

large independent variables

• a sample size that is greater than or equal to 30

• 

null hypothesis H ₀

• μ₁ is equal to μ₂

• μ₁ - μ₂ = 0

alternative hypothesis H_a

μ₁ is not equal to μ₂

z-test

used to determine any difference between two population means

standard error

the variability of the sample mean across different samples

What does H_0 represent?

1. Null hypothesis

2. Standard error

3. Alternative hypothesis

4. Standard deviation

Null hypothesis

The variability of individual observations around their mean is known as the:

1. Standard deviation

2. Alternative hypothesis

3. Z-value

4. Null hypothesis

Standard deviation

Kelly lives in Newark and commutes to New York City. She notices that the price of coffee seems to be different in the two cities. She buys 39 coffees in Newark and finds that they have an average price of $1.50, with a standard deviation of 25 cents. She buys 41 coffees in New York City and finds that they have an average price of $2.25, with a standard deviation of 50 cents. At a significance level of 0.05, is there a significant difference between the prices of coffee in the two cities? What are the relevant z-scores that lead you to your conclusion?

1. No, there isn't a significant difference; 8.55 > 1.96

2. Yes, there's a significant difference; 8.55 > 1.96

3. No, there isn't a significant difference; 1.43 < 1.96

4. Yes, there's a significant difference; 1.43 < 1.96

Yes, there's a significant difference; 8.55 > 1.96

The variability of the sample mean across different samples is called the:

1. Z-value

2. Standard deviation

3. Alternative hypothesis

4. Standard error

Standard error

What does H_A represent?

1. Standard error

2. Z-value

3. Alternative hypothesis

4. Null hypothesis

Alternative hypothesis

hypothesis testing

designing a study and analyzing the data in order to see if your scientific prediction is correct

null hypothesis

• the hypothesis that a person starts with

• what the researcher believes to be true

alternative hypothesis

the opposite of the null hypothesis

mean

the average of the two groups

When calculating the t statistic, Kris is confused. For x-bar, he should put the mean of _____, and for mu, he should put the mean of _____.

1. Another study; his study

2. The population; his study

3. His study; another study

4. His study; the population

His study; the population

Julie has done a study and her t statistic is smaller than the number in the t-table. This means that Julie should:

1. Reject the null hypothesis

2. Accept the null hypothesis

3. Reset the significance level

4. Do the study over

Accept the null hypothesis

Sherri is doing a study. She believes that the subjects in her study will do about the same as the entire population would. Thus, the belief that Sherri's mean does not differ from the population's mean is the _____ hypothesis, and the belief that Sherri's mean is significantly different from the population's mean is the _____ hypothesis.

1. Researcher's; population

2. Null; alternative

3. Population; researcher's

4. Alternative; null

Null; alternative

Khan is designing a study and needs to operationalize his variables. Which of the following variables is already operationalized?

1. Height in inches

2. Intelligence

3. Happiness

4. Beauty

Height in inches

Which of the following is NOT an appropriate significance level for a study?

1. 0.25

2. 0.05

3. 0.01

4. 0.10

0.25

hypothesis testing

the formal procedure used by statisticians to test whether a certain hypothesis is true or not

Type I error

• null hypothesis is false when it actually is true

• you are wrongly thinking that the null hypothesis is false

null hypothesis

the hypothesis for our expected outcome

type II error

• null hypothesis is true when it actually is false

• you are wrongly thinking that the null hypothesis is true

Which of the following represents the probability of making a type II error?

• α

• β

• S

• P

• L

β

Which of the following represents the probability of making a type I error?

• α

• β

• S

• P

• L

α

How many types of errors can be made when interpreting statistical results?

1. Three

2. Four

3. One

4. None

5. Two

Two

A scientist publishes a paper where they assert that their null hypothesis about the speeds required for clouds to form is false. They later find that clouds actually form much more quickly than they'd described in the paper, closer to the speeds described in the null hypothesis. What sort of error did the scientist make, and why?

1. Type I, because their findings show that the null hypothesis is false when it's actually true.

2. Type I, because their findings show that the null hypothesis is true when it's actually false.

3. Type II, because their findings show that the null hypothesis is false when it's actually true.

4. Type II, because their findings show that the null hypothesis is true when it's actually false.

Type I, because their findings show that the null hypothesis is false when it's actually true.

When is a type II error made?

1. When your findings show that the null hypothesis is true when it actually is false.

2. When your findings show that the null hypothesis is false when it is false.

3. When your findings show that the null hypothesis is true when it is true.

4. When your findings show that the null hypothesis is false when it actually is true.

When your findings show that the null hypothesis is true when it actually is false.

Statistically Significant

the difference in the results did not occur by random chance

Random Chance

these results would only occur by chance less than 1 in 20 times, or .05

Two-Tailed Test / Non Directional Hypothesis

the standard test of significance to determine if there is a relationship between variables in either direction

One-Tailed Test Directional Hypothesis

test of significance to determine if there is a relationship between variables in one direction

In statistical equations, probability is usually represented by _____.

1. the word probability

2. a lower case p

3. the alpha symbol

4. the abbreviation py

a lower case p

A civil engineer is trying to prove that his new method of laying blocks is more effective than the traditional method. The engineer will conduct a:

1. Two-tailed test

2. One-tailed test

3. Random test

4. Point estimate

One-tailed test

Which of the following statements best describes 'statistical significance'?

1. The p value is greater than the significance level.

2. The difference in the results occurred by random chance.

3. The difference in the results did not occur by random chance.

4. How researchers determine if they should accept their null hypothesis.

The difference in the results did not occur by random chance.

The _____ is a test where all of the significance is on only one side of the bell curve.

1. chi-square test

2. one-tail test

3. t-test

4. two-tail test

one-tail test

Why is a two-tailed test sometimes referred to as the non-directional hypothesis?

1. Because researchers are unsure of what to do with their data.

2. Because this test only verifies if there is a statistically significant difference between groups or not.

3. Because two-tailed tests are conducted when the results are both positive and negative.

4. Because this test determines if there is a statistically significant difference between groups in either direction.

Because this test determines if there is a statistically significant difference between groups in either direction.

z-tests | t-tests

statistical methods involving data analysis

z-tests

statistical calculations that can be used to compare population means to a sample’s

t-tests

determine if there is a statistical significant difference between two independent sample groups

What are z-tests and t-tests?

1. Statistical calculations that can be used to test a hypothesis

2. Geometric tests

3. College entrance tests

4. Tests of the alphabet

Statistical calculations that can be used to test a hypothesis

Which statistical method could you use when you have a normal distribution of the data?

1. t-test or z-test

2. t-test

3. neither t-test nor z-test

4. z-test

t-test or z-test

You want to test if your tomato plants grow quicker when they are fertilized, so you will fertilize five of your plants and you will not fertilize the other five. Which statistical test should you use?

1. z-test

2. t-test or z-test

3. none of the answers are correct

4. t-test

t-test

When are t-tests most appropriate to use?

1. all the answers are correct

2. when we want to compare two independent samples

3. when we want to find out if the difference in the results is due to chance

4. when the sample size is small (n<30)

all the answers are correct

If a problem provides a mean, a standard deviation, and a sample size larger than 30, which method should be used?

1. none of the answers are correct

2. x-test

3. t-test

4. z-test

z-test

Null Hypothesis

the prediction that there is no interaction between variable

Alternative Hypothesis

the prediction that there is a measurable interaction between variables

Standard Deviation

a number corresponding to a bell curve describing how spread out the data is

Degrees of Freedom

the number of scores used after calculation

How many degrees of freedom are lost when calculating the t-value?

1. 3

2. 4

3. 5

4. 2

2

A group of seven people have taken a quiz and their scores are 8,9,10,5,8,9 and 10. Calculate the standard deviation.

1. 1.6

2. 2.9

3. 8.4

4. 2.5

1.6

When are degrees of freedom lost?

1. When calculating standard deviation.

2. When calculating the mean.

3. When calculating the t-value.

4. When calculating variance.

When calculating standard deviation.

Which of the following simple statements most appropriately describes the null hypothesis?

1. There is no difference between the individuals.

2. There is a difference between the individuals.

3. There is a difference between the groups.

4. There is no difference between the groups.

There is no difference between the groups.

Some high school students were divided into two groups, group A and group B, and given the same test.

Group A consisted of 6 students and the average score was 12 with a standard deviation of 2. Group B consisted of 8 students and the average score was 11 with a standard deviation of 3. The variability within the groups is:

1. 1.125

2. 1.339

3. 1.792

4. 0.667

1.339

proportion

a look at a portion or a part in relation to the whole

hypothesis testing for a proportion

• to perform a statistical analysis to help us answer questions

• used to find the possibility of a mutually exclusive outcome for a larger population

conditions

things that have to be true in order for the test to be valid or useful

p

the probability of an outcome

mutually exclusive

either one or the other possible outcome must be true

Which of the following is an example of a question that may be answered using hypothesis testing for a proportion?

1. What are the chances of turning up a jack as my next card?

2. How many people will be coming to my wedding?

3. Are more than 80% of pet owners happy?

4. What is a person's mood most likely to be when they wake up?

Are more than 80% of pet owners happy?

In the z-test formula, what does n stand for?

1. Sample size.

2. Hypothesized value.

3. Observed sample proportion of successes.

4. Standard normal distribution.

Sample size

Why are proportions useful?

1. Because they allow us to establish with certainty the behavior of a population.

2. Because they allow us to look at a smaller sample of a population and determine the behavior of the larger population.

3. Because they allow us to establish with certainty the behavior of a sample of a population.

4. Because they allow us to look at a smaller sample of a population and determine what the larger population is likely to do.

Because they allow us to look at a smaller sample of a population and determine what the larger population is likely to do.

What are the two hypotheses that must be created when performing hypothesis testing for a proportion?

1. Null and alternate.

2. p and z.

3. Null and p value.

4. Alternate and z value.

Null and alternate.

Which of these is NOT a condition for using hypothesis testing for a proportion?

1. At least 10 successes and 10 failures.

2. Population at least 10 times as big as the sample.

3. Random sample.

4. Mutually exclusive outcomes.

Population at least 10 times as big as the sample.

standard error

a measure of how variable the sample mean can be across different samples of a given population

Z-test

Step 1: State your hypothesis

Step 2: Find your critical values

Step 3: Calculate the test value

Step 4: Make your decision - do you reject or fail to reject the null hypothesis?

Step 5: Summarize your results

p hat is a symbol used to represent which of the following?

1. Sample proportion

2. Sample mean

3. Sample size

4. Population mean

5. Population proportion

Sample proportion

Based on the lesson, n is a symbol commonly used to denote which of the following?

1. Population proportion

2. Sample mean

3. Null hypothesis

4. Sample proportion

5. Sample size

Sample size

To use the z-test for finding a difference in population proportions, we must ensure which of the following?

1. The populations are equal in size.

2. The samples are independent.

3. The samples are dependent.

4. The samples are of the same size.

5. The populations have different sizes.

The samples are independent.

A recent study shows that in 25 out of 50 national parks, there was at least one rare bird sighting in the last ten years, while in 275 out of 500 state parks, there was at least one rare bird sighting in the last ten years. Using a significance level of 0.05, is there any difference in the proportion of national and state parks with at least one rare bird sighting in the last ten years, and what are the relevant z-scores?

1. There is a difference; -1.96 < -0.68 < 1.96

2. There is no difference; -9.17 < -1.96

3. There is no difference; -1.96 < -0.68 < 1.96

4. There is a difference; -9.17 < -1.96

There is no difference; -1.96 < -0.68 < 1.96

Which of these best represents the null hypothesis?

1. p ₁ is equal to p ₂

2. The sample size

3. p ₁ is not equal to p ₂

4. X ₁

5. H _A

p 1 is equal to p 2

paired or matched samples

two dependent samples, those where each sample’s data value is collected from the same source

Which of these is an example of paired data?

1. The difference in exam scores between male and female students

2. The difference in IQ scores of people born in different years

3. Five people being tested for the efficacy of a drug before and after treatment

4. The difference between the speeds of runners based on two different age groups

Five people being tested for the efficacy of a drug before and after treatment

What does n stand for in hypothesis testing?

1. Test statistic

2. The total number of unpaired sample differences

3. Standard deviation

4. The total number of paired sample differences

The total number of paired sample differences

A researcher is interested in the cognitive performance of teenagers, and collects data from students from two different schools. For each student at the first school, the researcher compares the results against a student at the second school. Is the researcher using matched samples? Why or why not?

1. Yes, they are, because the first sample school is being matched to a second sample school.

2. No, they're not, because the data values are being collected from two different schools, and hence two different sources.

3. Yes, they are, because each member of one sample is being matched to a member of the second sample.

4. No, they're not, because the students don't necessarily ever meet, even if the researcher is comparing their results.

No, they're not, because the data values are being collected from two different schools, and hence two different sources.

Which of the following are synonyms?

1. Independent samples; matched samples

2. Paired data; independent samples

3. Paired data; twinned data

4. Paired data; matched samples

Paired data; matched samples

In the equation for the test statistic of matched pairs, s_d stands for the:

1. Test statistic

2. Degrees of freedom

3. Critical value

4. Standard deviation

Standard deviation

hypothesis testing

is often used to test the relationship between two variables

null hypothesis H₀

constructed to indicate that there is not a statistical difference between two populations or measurements

alternative hypothesis H_A

are mutually exclusive, so that accepting or rejecting one has the opposite effect on the other

critical region

an area far away from the center of the distribution

two-tailed test

looks at both sides of the distribution

What are the two hypotheses used in hypothesis testing?

1. The null hypothesis and the positive hypothesis

2. The original hypothesis and the alternative hypothesis

3. The null hypothesis and the alternative hypothesis

4. The negative hypothesis and the positive hypothesis

The null hypothesis and the alternative hypothesis

What type of comparison test should be used if you are assessing whether or not your data is greater than some stated value?

1. This is not a valid hypothesis test

2. The null test

3. A two-tailed test

4. A one-tailed test

A one-tailed test

Which of these values is most commonly used for the significance level in hypothesis testing?

1. 25%

2. 90%

3. 5%

4. 50%

5%

In hypothesis testing, data that falls into the critical region is used for what purpose?

1. To define the critical parameters for the test

2. To accept the null hypothesis

3. To reject the null hypothesis

4. To reject the alternative hypothesis

To reject the null hypothesis

What value should be pre-selected for comparison purposes when running a hypothesis test?

1. The alternative hypothesis

2. The significance level

3. The Z-statistic

4. The statistical error

The significance level