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(Answered)-Hi I wanted help with the first problem. Specifically section h.


Hi I wanted help with the first problem. Specifically section h. but It would be nice to explain the other steps for confirmation.?


Hypothesis Testing and Single Sample z test Practice Problems

 


 

Note: unless indicated otherwise, use level of significance of .05 for all questions

 

1. A study was conducted to investigate whether the underperformance of students in high

 

schools in the United States can be reduced. There has been recent interest in the issue of

 

?mindsets? to improve academic performance. It has been shown that individuals with a

 

?growth mindset? (i.e., a belief that students can grow their intelligence and that academic

 

challenges are an opportunity for growth, rather than a sign that the student is not capable of

 

learning) may do better in school than those with a ?fixed mindset? (i.e., a belief that students

 

are born with a fixed level of ability that cannot be changed). To examine this issue, a

 

research study was conducted in which a group of 49 high school students were given a 45

 

minute ?growth mindset intervention? in which they were taught that the brain can grow and

 

reorganize as a result of hard work and academic challenges. At the end of the school year,

 

the GPA of a sample of students who were given the ?growth mindset intervention? was

 

compared to the overall GPA of all students at the high school. It is known that the overall

 

GPA of students at the high school is 2.40 with a SD of .25. Complete the following steps to

 

conduct a statistical test that addresses if the ?growth mindset intervention? leads to a

 

difference in the GPA in high school students.

 

a. What is the Independent Variable (IV) with its respective levels and what is the

 

Dependent Variable (DV) in this experiment?

 

b. Step 1: Write the null and research (alternative) hypotheses in symbols.

 

c. Step 2: Assume that we draw all possible random samples of 49 students from the

 

population of students at the high school. What would be the appropriate (i.e., compute)

 

standard error (SE) for a distribution of samples of size 49? Give an interpretation in

 

words of what this number means.

 


 

d. Step 2 (continued): The critical value for the test statistic.

 

e. Step 3: Find the obtained (i.e., computed) test statistic for a sample (n=49) with a mean

 

of 2.50.

 


 

Step 4: Make a statistical decision about the null. Will you reject or fail to reject the null based

 

on your sample data? (Be sure to include appropriate test statistic and decision criteria).

 

f. Step 4 (continued): Provide a substantive conclusion about the results from your sample

 

data. (Be sure to include the research context and descriptive statistics).

 

g.

 


 

Continuing with this example, (i.e. the same population mean, standard deviation, etc.),

 

calculate the effect size of the test anxiety on GPS (using Cohen?s d) for the sample of

 

students in the ?growth mindset intervention group? who had a mean GPA of 2.50. How

 

large of an effect size is this, small, medium, or large?

 


 

h. The following table lists the possible decisions that can be made based on the research

 

study above. Label which boxes would be correct decisions and which would be errors

 

(Type I and Type II).

 

Truth

 

H0 True

 


 

H0 False

 


 

?Growth Mindset

 

Intervention? does not

 

affect GPA

 


 

?Growth Mindset

 

Intervention? does

 

affect GPA

 


 

Reject H0

 

?Growth

 

Mindset

 

Intervention

 

? does affect

 

GPA

 

Statistical

 

Decision

 


 

i.

 

j.

 


 

Fail to reject

 

H0

 

?Growth

 

Mindset

 

Intervention

 

? does not

 

affect GPA

 

What would a Type I error mean in the context of this study?

 

What would a Type II error mean in the context of this study?

 


 

2. The national average for students on the Science Attitudes Questionnaire is 10.0, with

 

a standard deviation of 1.0. Creative Teaching Elementary School has created a new

 

textbook which they use in their school because they believe it will increase student

 

interest in science. A random sample of 25 students from Creative Teaching

 

Elementary School are given the Science Attitudes Questionnaire and their mean

 

score was 10.2. Go through all 4 steps of hypothesis testing to decide if the new

 

textbook at Creative Teaching Elementary School significantly impacts students?

 

attitudes about math.

 

a. Step 1: Write out the hypotheses

 

b. Step 2: Assume that we draw all possible random samples of 25 students from the

 

population of students at the college. What would be the appropriate standard error (SE)

 

for a distribution of samples of size 25?

 

c. Step 2 (continued): What is the critical value for this test statistic?

 

d. Step 3: Calculate the test statistic

 


 

e. Step 4: Make a statistical decision about the null. Will you reject or fail to reject the null

 

based on your sample data? (Be sure to include appropriate test statistic and decision

 

criteria).

 


 

f. Step 4 (continued): Provide a substantive conclusion about the results from your sample

 

data. (Be sure to include the research context and descriptive statistics).

 


 

g. The following table lists the possible decisions that can be made based on the research

 

study above. Label which boxes would be correct decisions and which would be errors

 

(Type I and Type II).

 

Truth

 

H0 True

 


 

H0 False

 


 

New Textbook at

 

Creative Teaching

 

Elementary School

 

does not affect student

 

attitudes about science

 


 

New Textbook at

 

Creative Teaching

 

Elementary School

 

does affect student

 

attitudes about science

 


 

Reject H0

 

New Textbook at

 

Creative Teaching

 

Elementary School

 

does affect student

 

attitudes about science

 

Statistical

 

Decision

 


 

Fail to reject H0

 

New Textbook at

 

Creative Teaching

 

Elementary School

 

does not affect

 

student attitudes about

 

science

 


 

h. What would a Type I error mean in the context of this study?

 


 

i. What would a Type II error mean in the context of this study?

 


 

 


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