Hypothesis Testing

Hypothesis Testing

By Santiago Randy

​Prayer

Statistics and Probability

Dear Lord and Father of all, Thank you for today. Thank you for ways in which you provide for us all. For Your protection and love we thank you. Help us to focus our hearts and minds now on what we are about to learn. Inspire us by Your Holy Spirit as we listen and write. Guide us by your eternal light as we discover more about the world around us. We ask all this in the name of Jesus.

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https://www.lords-prayer-words.com/family/prayer_before_class.html

Poll

How are you feeling today?

• I'm feeling great!

• I'm doing fine but could be better

• I don't know

• I'm good

• I'm struggling

Online Class Reminders

​​Be prepared for class

​​Be respectful

​​Keep your microphone on mute

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​​Be responsible in the chat box

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​​Be fully present

​​Inspire one another

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Would You Rather!

​ be a girl or a boy?	​ have more siblings or be the only child?	​ go to college or get a job?
​ come to school or hang out with your friends?	​ go without Facebook or junk food for the rest of your life?	​ have many good friends or one best friend?

​Learning Objectives:

At the end of the lesson, you are expected to:

a.    Identify the steps in hypothesis testing

b. Solve problems involving test of hypothesis on the population mean

c. Recognize the importance of decision-making process​

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

Which of the following will produce a correct decision?

• rejecting a false hypothesis

• failure to reject a false hypothesis

• rejecting a true null hypothesis

• failure to reject a true null hypothesis

Multiple Choice

If a result is said to be significant at 5% level, what does it mean?

• The null hypothesis is 5% true

• We fail to reject the false null hypothesis 5% of the time

• The null hypothesis is 5% incorrect

• There is a 5% probability that a true null hypothesis is rejected

Multiple Choice

Which value separates the critical region from the non-critical region in a normal curve when testing a hypothesis?

• t-value

• z-value

• critical value

• computed value

Multiple Choice

What should be the decision if the computed z-value lies in the critical region?

• Reject the null hypothesis

• Do not reject the null hypothesis

• Reject the alternative hypothesis

• Do not reject the alternative hypothesis

Multiple Choice

The mean height of women is greater than 64" (inches). Which of the following represents the null and alternative hypotheses?

• H0: μ > 64"

  Hₐ: μ ≠ 64"

• H0: μ = 64"

  Hₐ: μ > 64"

• H0: μ > 64"

  Hₐ: μ ≠ 64"

• H0: p = 64"

  Hₐ: p > 64"

Multiple Choice

What is the last step in the hypothesis testing procedure?

• Draw conclusion

• State the null and alternative hypotheses

• Choose the level of significance

• Determine the test statistic and compute it

Multiple Choice

Perform a hypothesis test on the null hypothesis where μ = 6.9. A random sample of 25 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed at α = .01.

• There is enough evidence to reject the claim

• There is not enough evidence to reject the claim

• There is enough evidence to support the claim

• There is not enough evidence to support the claim

Multiple Choice

In a right-tailed test, what will you do if the critical value is greater than the computed value?

• Reject the null hypothesis

• Do not reject the null hypothesis

• Reject the alternative hypothesis

• Fail to reject the alternative hypothesis

Multiple Choice

If the t-computed value is 1. 093 and the critical value is 1.699, what will be the decision?

• Reject the null hypothesis

• Do not reject the null hypothesis

• Support the null hypothesis

• Support the alternative hypothesis

Multiple Choice

What is the first step in the hypothesis testing procedure?

• Draw conclusion

• State the null and alternative hypotheses

• Choose the level of significance

• Determine the test statistic and compute it

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Find the Word... That's the Word!

Directions: Find the words related to hypothesis testing. The letters consisting the word may be arranged horizontally, vertically, or diagonally. Make sure to identify each of them.

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Hypothesis Testing

1. State the null hypothesis (H_o) and Alternative hypothesis (H_a).

2. Determine the test statistic that will be used to conduct the hypothesis testing. Then, calculate its value.

3. Find the critical value for the test and draw critical region.

4. Decide and draw conclusion.

Example 1:

According to a study conducted by the Grade 12 students, Php155 is the average monthly expense for cell phone loads of high school students in their province. A Statistics student claims that this amount has increased since January of this year. Do you think his claim is acceptable if a random sample of 50 students has an average monthly expense of Php165 for cell phone loads? Using 5% level of significance, assume that a population standard deviation is Php52.

​Step 1:

State the null and alternative hypothesis

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Given: 𝑥̅= 165 𝜇 = 155 𝜎 = 52 𝑛 = 50 𝛼 = 0.05

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𝐻𝑜: 𝜇 = 155 𝐻𝑎: 𝜇 > 155

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Subject | Subject

Some text here about the topic of discussion

​Step 2:

Determine the test statistic, then compute its value.

​Given: 𝑥̅= 165 𝜇 = 155 𝜎 = 52 𝑛 = 50 𝛼 = 0.05

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Subject | Subject

Some text here about the topic of discussion

​Step 3:

Find the critical value and draw the critical region.

Subject | Subject

Use t he z-critical value table.

​Step 4:

Draw a conclusion.

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The z-computed value is 1.361 and it lies within the non-rejection region, so we fail to reject the null hypothesis. Therefore, there is no enough evidence to support the claim that the average monthly expense for cell phone loads is more than ₱155. This result is significant at 𝛼 = 0.05 level.

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Statistics and Probability

Poll

How are you feeling:

• Keep going, I understand

• I'm a little confused

• Stop, I need help

Example 2:

Blood glucose levels for obese teenagers have a mean of 120. A researcher thinks that a diet high in raw cornstarch will have a positive or negative effect on blood glucose levels. A sample of 25 patients who have tried the raw cornstarch diet has a mean glucose level of 135 with a standard deviation of 38. Test the hypothesis at 𝛼 = 0.10 that the raw cornstarch had an effect.

​Step 1:

State the null and alternative hypothesis

Given: 𝑥̅= 135 𝜇 = 120 𝑠 = 38 𝑛 = 25 𝛼 = 0.10 𝑑𝑓 = 24​

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𝐻𝑜: 𝜇 = 120 𝐻𝑎: 𝜇 ≠ 120

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Subject | Subject

Some text here about the topic of discussion

​Step 2:

Determine the test statistic, then compute its value.

𝑥̅= 135 𝜇 = 120 𝑠 = 38 𝑛 = 25 𝛼 = 0.10 𝑑𝑓 = 24​

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Subject | Subject

Some text here about the topic of discussion

​Step 3:

Find the critical value and draw the critical region.

Subject | Subject

Use t he z-critical value table.

​Step 4:

Draw a conclusion.

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Since the t-computed value is 1.974 which is greater than the critical value of 1.711, we reject the null hypothesis and support the alternative hypothesis. We can conclude that there is enough evidence to support the claim that the raw cornstarch had an effect on blood glucose levels.

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Statistics and Probability

Poll

How are you feeling:

• Keep going, I understand

• I'm a little confused

• Stop, I need help

​Please correct me if I'm wrong!

GRASP task.

Goal: The goal is to solve a real-life problem involving hypothesis testing.

Role: You are an academic tutor

Audiences: The target audience is your classmate who needs help about the topic hypothesis testing

Situation: One of your classmates were not able to attend the online class. He is struggling answering the task given by your teacher. As an academic tutor he asks you for some feedback regarding his answer.

Product:  You need to make feedback (written or record) on your classmate’s answer.

Open Ended

Type your feedback here :)

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​​Cloudy

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​​Rainy

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​​Windy

​​Stormy

​>One (1) thing you really love about our topic

1-4-3 (iloveyou) Chart

Some text here about the topic of discussion

​>Four (4) important reasons why you love our topic

>Three (3) things you still need to understand about our topic

Multiple Choice

What is the first step in the hypothesis testing procedure?

• Draw conclusion

• State the null and alternative hypotheses

• Choose the level of significance

• Determine the test statistic and compute it

Multiple Choice

What is the third step in the hypothesis testing procedure?

• Draw conclusion

• Determine the test statistic and compute it

• State the null and alternative hypothesis

• Find the critical value for the test; then draw the critical region

Multiple Choice

In the hypothesis testing procedure, drawing a conclusion should always be the __________ step.

• first

• second

• third

• last

Multiple Choice

After formulating the hypothesis, what is the next step in the hypothesis testing procedure?

• Draw conclusion

• Determine the test statistic and compute it

• Choose the level of significance

• Find the critical value and draw the critical region

Multiple Choice

The null hypothesis is rejected. What does it mean?

• The null hypothesis is incorrect

• The alternative hypothesis is true

• There is enough evidence against the null hypothesis

• There is a very small probability that the null hypothesis is true

Multiple Choice

In a left-tailed test, what will you do if the critical value is less than the computed value?

• Reject the null hypothesis.

• Reject the alternative hypothesis

• Do not reject the null hypothesis.

• Do not reject the alternative hypothesis

Multiple Choice

It is a value that separates the acceptance region from the rejection region in a normal curve when testing the hypothesis?

• t-value

• critical value

• z-value

• computed value

Multiple Choice

What should you do if the computed z-value lies in the critical region?

• Reject the null hypothesis

• Do not reject the null hypothesis.

• Reject the alternative hypothesis.

• Do not reject the alternative hypothesis.

Multiple Choice

The mean height of women is less than 64" (inches). Which of the following represents the null and alternative hypotheses?

• H0: μ > 64"

  Hₐ: μ < 64"

• H0: μ = 64"

  Hₐ: μ > 64"

• H0: μ = 64"

  Hₐ: μ < 64"

• H0: p = 64"

  Hₐ: p < 64"

Multiple Choice

Perform a hypothesis test where the null hypothesis is that the μ = 6.9. A random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed at α = 0.05.

• There is enough evidence to reject the claim

• There is not enough evidence to reject the claim.

• There is enough evidence to support the claim

• There is not enough evidence to support the claim.

Performance Task No. 6

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GOAL:

Your goal is to help SHS learners in understanding the topic solving problems in hypothesis testing.

ROLE:

You are the president of Mathematics Club.

AUDIENCE:

The target audiences are SHS students taking up Statistics and Probability.

SITUATION:

Mathematics clubs play an important role in building positive relationships between teachers and student. As the president of the mathematics club, you want to develop students’ level of mathematics skills and knowledge through giving infographic chart that gives an easy-to-understand overview of topics.

PRODUCT:

You will create an infographic chart about solving problems in hypothesis testing.

STANDARD: Your output will be graded using a rubric.​

" YOU are great! "