## An SAT prep course claims to improve the test score of students

An SAT prep course claims to improve the test score of students. The table below shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her verbal SAT scores. Do these results support the claim that the SAT prep course improves the students' verbal SAT scores?
Let d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course)
. Use a significance level of α=0.05 for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.
Student Score on first SAT Score on second SAT
1 380 420
2 440 530
3 470 530
4 490 550
5 440 460
6 420 490
7 410 430

a. State the null and alternative hypotheses for the test.
b. Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.
c. Compute the value of the test statistic. Round your answer to three decimal places.
d. Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.
e. Make the decision for the hypothesis test.

## Week 11 Assignment 1: Which Tools Shall You Use?

Overview

As part of continuing your work on your evidence-based project proposal, identify one to three outcomes of interest. That is,what you hope to change or improve based on the implementation of your project (your project’s dependent variable). For example, if you are designing an intervention to reduce hospital re-admission rates for patients with heart failure, the outcome is re-admission rates. Another example would be a mindfulness-based intervention for critical care nurses to reduce burnout; in this case, burnout is the outcome of interest.

Once you have identified the outcomes of interest in your project, you need to determine how each outcome will be measured. Consider the examples above. How might you measure re-admission rates? (For example, you might measure the percentage of patients with heart failure who are re-admitted with a diagnosis of heart failure within 90 days of being discharged). How about measuringburnout in critical-care nurses? (Would you use the Maslach Burnout Inventory, or some other tool?). As you can see, there are different ways to measure outcomes.

The Maslach Burnout Inventory is an example of a measurement tool. Many tools such as this exist to measure a variety of phenomena such as resilience, moral distress, self-efficacy, and many others! These tools can include surveys or questionnaires that have been used in the literature to evaluate similar evidence-based practice projects. Many tools may be available to you depending on your topic. This assignment involves you searching the databases to learn about how your topic has been evaluated in the past.

To find tools and determine how outcomes can be measured, start by reading the literature. What tools are frequently used to assess the variables or outcomes of interest? Some are very commonly used. When you find a tool, you’ll want to review the original primary source —the published (or revised and updated) book or article where the tool was first described. Evaluate how the tool was developed and if it was found to be reliable and valid. It is very interesting to read instrument-development articles, so please do if you get the chance! Often the titles of these articles contain the terms “development and psychometric testing of the _ scale/tool.” Please note when actually conducting research that there are many considerations for the selection and use of measurement tools, including permission to use the tool from the researcher.

Assignment Instructions

For this assignment, select one to three outcomes and identify how each outcome will be measured. How many outcomes you have depends on your individual project.

As discussed, you might need to determine exactly how certain outcomes will be measured (such as re-admission rate). It is also possible that there is no tool available to measure an outcome of interest in your study. For example, if I wanted to assess “knowledge” of some topic, I would need to create questions to obtain data about this outcome. In either case, include the following information:

Clearly state the outcome and how, specifically, you will measure it.
Describe why you selected the measurement method and how you plan to use it in the project.

If you are able to identify an appropriate measurement tool that already exists (such as the Maslach Burnout Inventory) for an outcome of interest, include the following information:

The outcome and the name of the tool that will be used to measure the outcome.
A brief description the tool. How many items are there? How are items scored? What do scores mean?
An explanation of why you selected this tool and how you plan to use it in your project.
The validity and reliability of the tool.

Here is an example:

Self-Efficacy. Self-efficacy will be measured using the General Self-Efficacy Scale (GSE) (Schwarzer & Jerusalem, 1995).

The scale was developed in 1979 and subsequently revised and adapted to 26 languages, and consists of 10 items, scored on a scale of 1 (not at all true) to 4 (exactly true), with a score range of 10 to 40 (where lower scores indicate lower self-efficacy and higher scores indicate higher self-efficacy) (The General Self-Efficacy Scale, n.d.).

In a sample of 747 early career nurses, the scale had a Cronbach’s alpha of 0.884 (Wang et al., 2017). This establishes reliability in that sample (early career nurses).

The GSE scale was selected because it offers a general overview of the concept of self-efficacy and is not specific to nursing practice. In the proposed study, the GSE scale will be given to participants before and after the intervention.

After you identify between two and five peer-reviewed tools, in a Microsoft Word document, describe in 300 to 500 words why you have selected them and how you plan to use them in your proposal. Include the validity and reliability of the tools (which is found in journal articles). Submit the names of the tools along with your 300- to 500-word justification and ensure that you use APA format.

## Submit this project to the proctor at the time you take Test 3.

When the problem involves hypothesis testing, use the following structure for written reports.

# Hypothesis testing steps

• Step 1: State the hypotheses.
• Step 3: Give the value of the test statistic and the p-value.
• Step 4: Use the p-value to draw a conclusion. State the conclusion in statistical
terms: Reject Ho in favor of Ha, or retain Ho (fail to reject Ho).
• Step 5: State the conclusion in layman terms and in context of the application. Use the
p-value to state the strength of the evidence.
When a significance level is not given, then use the following guidelines and language associated
with p-value. Note that the lower the p-values, the stronger the evidence against Ho and in
favor of Ha. We go from insufficient evidence, to some evidence, to fairly strong evidence, to
strong evidence, to very strong evidence.
• p-value > .10
retain Ho – there is insufficient evidence to reject Ho in favor of Ha
• .05 < p-value ≤ .10
gray area -- decision to reject Ho or retain Ho is up to the investigators – there is some
evidence against Ho and in support of Ha
• .01 < p-value ≤ .05
reject Ho in favor of Ha – there is fairly strong evidence against Ho and in favor of Ha
• .001 < p-value ≤ .01
reject Ho in favor of Ha – there is strong evidence against Ho and in favor of Ha
• p-value ≤ .001
reject Ho in favor of Ha – there is very strong evidence against Ho and in favor of Ha
Use your TI-83/TI-84 calculator for all of these problems. You will not need any tables.
Use the Sample Test 3 Questions—Answer Key (posted in Canvas) as an example of what my
expectations are.

1. A sociologist suspects that, for married couples with young children, the husbands watch more TV
than the wives. Twenty married couples are randomly selected and their weekly viewing times, in
hours, are recorded in the table below. Assume the population of differences between husband’s
and wife’s TV time is mound-shaped and symmetrical.
a) Do the sample results provide sufficient evidence to support the sociologist’s claim? Perform a
hypothesis test to find out.
b) If there is sufficient evidence to support the sociologist’s claim, estimate how much more TV the
husbands watch, on average, with a 95% confidence interval. Interpret.

1. The data below show the sugar content (as a percentage of weight) of several national brands of
children’s and adults’ cereals. Assume the distributions of sugar content in both children’s cereals
and adults’ cereals are mound-shaped and symmetrical.
a) Does the sample data provide sufficient evidence to conclude that the sugar content in
children’s cereals is higher than that in adults’ cereals, on average? Perform a hypothesis test to
find out.
b) If you conclude that children’s cereals have more sugar than adults’ cereals, estimate how much
more with a 95% confidence interval for the difference in mean sugar content. Interpret.
Children’s cereals: 40.3, 55, 45.7, 43.3, 50.3, 45.9, 53.5, 43, 44.2, 44, 47.4, 44, 33.6, 55.1, 48.8,
50.4, 37.8, 60.3, 46.6
Adults’ cereals: 20, 30.2, 2.2, 7.5, 4.4, 22.2, 16.6, 14.5, 21.4, 3.3, 6.6, 7.8, 10.6, 16.2, 14.5, 4.1,
15.8, 4.1, 2.4, 3.5, 8.5, 10, 1, 4.4, 1.3, 8.1, 4.7, 18.4
2. A randomly selected sample of entering college freshmen has participated in a special program to
enhance their academic abilities, and their GPAs at the end of one year have been recorded. A
group of 20 students from the same class who did not participate in the program has been selected
as a control group, and they have been matched with the experimental group by gender, age, highschool class rank, ACT scores, and declared major. The results (GPAs) are presented below. Assume
the population of differences between the project student GPA and the control group student GPA
is mound-shaped and symmetrical.
a) Can the program claim that it was successful? Carry out a hypothesis test to find out.
b) If you conclude that the program was successful, make a judgment regarding the size of the
effect of program participation on student GPAs by constructing a 95% confidence interval.

1. Michelle Sayther is a fashion design artist who designs the display windows in front of a large
clothing store in New York City. Electronic counters at the entrances total the number of people
entering the store each business day. Before Michelle was hired by the store, the mean number of
people entering the store each day was 3218. Management would like to investigate whether this
number has changed since Michelle has started working. A random sample of 42 business days after
Michelle began work gave an average of 𝑋𝑋� = 3392 people entering the store each day. The sample
standard deviation was s = 287 people. Assume the population of daily number of people entering
the store is mound-shaped and symmetrical.
a) Perform a hypothesis test to decide if the average number of people entering the store each day
since Michelle was hired is different from what it was before Michelle was hired.
b) If you find that the average number of people entering the store each day since Michelle was
hired is different from what it was before Michelle was hired, estimate the average number of
people entering the store each day since Michelle was hired with a 95% confidence interval and
interpret. (Has the number of people entering the store each day increased or decreased since
Michelle was hired, and by how much has it increased or decreased?)
2. An experiment was conducted to evaluate the effectiveness of a treatment for tapeworm in the
stomachs of sheep. A random sample of 24 worm-infected lambs of approximately the same age
and health was randomly divided into two groups. Twelve of the lambs were injected with the drug
and the remaining twelve were left untreated. After a 6-month period, the lambs were slaughtered
and the following worm counts were recorded. Assume the distribution of worm counts of drugtreated sheep is mound-shaped and symmetrical. Assume the distribution of worm counts of
untreated sheep is also mound-shaped and symmetrical.
c) Does the sample data provide sufficient evidence to conclude that the treatment is effective in
reducing the occurrence of tapeworm in sheep? Perform a test of significance to find out.
d) If you conclude that the treatment is effective, estimate the average reduction in tapeworm
count with a 95% confidence interval. Interpret.

1. In each of the problems above, #1- #5, an assumption of normality is made about the distribution of
the population(s) from which the sample data is obtained. For each of #1 - #5, provide the page
number in the e-book where the assumption is described by the author. You will be citing page
numbers from Sections 9.2, 10.1, and 10.2.
2. A study of the health behavior of school-aged children asked a sample of 15-year-olds in several
different countries if they had been drunk at least twice. The results are shown in the table, by
gender. (Health and Health Behavior Among Young People. Copenhagen. World Health
Organization, 2000)
a) Perform a hypothesis test to determine if there is a gender effect. That is, is there a difference
in the average percent of 15-year-old males who have been drunk at least twice and the average
percent of 15-year-old females who have been drunk at least twice? Assume the distributions
for both males and females are mound-shaped and symmetrical.
b) If there is sufficient evidence that there is a difference between average percent of 15-year-old
males who have been drunk at least twice and the average percent of 15-year-old females who
have been drunk at least twice, estimate the difference with a 95% confidence interval and

Quantitative project reasoning solutions. The following solutions have been provided to you by MyMathLab statistics experts The solutions were provided under the MyMathLab answers statistics help services.

## Estimate the linear effect of dose

Background: This second part of the assignment requires some more theoretical work based on fitting a linear regression model to investigate the effect of three dosage levels on an outcome. Suppose a clinical investigator is interested in examining the relationship between the effect of increasing doses of vitamin D supplement given to individuals who are Vitamin-D deficient. She performs a randomised trial in which she allocates (at random) volunteers to three groups, 1000 IU (International Units), 2000 IU and 3000 IU of supplement, per day for a perion of three months, after whcih the serum levels of a key metabolite of Vitamin D called 25 (OH) D are measured in each participant. (N.B. This is a hypothetical scenrio based on a real question that is current in epidemiology at the moment.)

Question 1
One possible analysis of the data described is to estimate the linear effect of dose, i.e to assume a linear relationship of expected outcome (labelled Y, as usual) to dose level, which for simplicity we will represent as X = 1,2,3 representing doses 1000IU, 2000IU, and 3000 UI respectively. To estimate the average rate of change in Y with dose we would fit the simple linear regression model with the standard assumptions for the error term:

Yi = Bo + B1x1 + ei

To objective is to show (algebraically) that if the sample size allocation between group1 1, group 2 and group 3 is 1:1:4 (i.e. n1-n, n2=n, n3 = 4n), then the leat squares estimate of B1 is

B1 = (4Y_bar3 - 3Y_bar1 - Y-bar2)/7

Question 2
The dataset provided contains some simulated data that might have arisen from the study just described, with 15 participants in groups 1, and 2, and 60 participants in dose group 3. Fit the regression model discussed above and demonstrate that the result obtained from B1 in question 1 is true in this sample.

Dataset for use in this assignment..
dosevd_reg_KA.xlsx

## example Question for estimating sample size

The state education commission wants to estimate the fraction of tenth-grade students that have reading skills at or below the eight grade level. In an earlier study, the population proportion was estimated to be 0.16.
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 99% confidence level with an error of at most 0.03? Round your answer up to the next integer.