#### Question Details

(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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