### T-Test and ANOVA Explanation#### T-Test for Paired SamplesThe formula for the t-test in paired samples is:\[ t = \frac{\sum D}{\sqrt{\frac{n(\sum D^2) - (\sum D)^2}{n-1}}} \]- **$n$**: Number of pairs of scores (e.g., if 8 people are measured at time 1 and time 2, then $df = 8 - 1 = 7$)- **$D$**: Difference between each pair of scores- **$\sum D$**: Sum of the differences- **$\sum D^2$**: Sum of the squares of the differences- $(\sum D)^2$: Square of the sum of differences#### Independent Samples T-TestThe formula for independent samples t-test is:\[ t = \frac{\overline{X}_1 - \overline{X}_2}{\sqrt{\frac{s_1^2}{n_1 - 1} + \frac{s_2^2}{n_2 - 1}}} \]- **$\overline{X}_1$**: Mean of the first group- **$\overline{X}_2$**: Mean of the second group- **$s_1^2$**: Sample variance of the first group- **$s_2^2$**: Sample variance of the second group- **$n_1$**: Number of subjects in the first group- **$n_2$**: Number of subjects in the second group*Note*: Ensure correct use of sample variances or standard deviations for accurate calculations.#### One Way ANOVA##### Between Groups Sum of SquaresSubtract the grand mean from each group mean, square the deviation, multiply by $n$, and add the values:\[ SS_B = \sum n (\overline{X}_n - \overline{X}_g)^2 \]- **$n$**: Number of subjects in a group- $\overline{X}_n$: Mean of a specific group- $\overline{X}_g$: Grand mean of all subjects##### Within Groups Sum of SquaresSubtract each group's mean from individual scores, square, and add them: **Study on Attention Span and Story Reading**An educational psychologist is exploring whether incorporating a child’s own name in a story influences their attention span during reading. In this study, six children were randomly assigned to read a story under ordinary conditions, using common and generic names. Another group of five children read versions of the same story where each child’s own name was substituted for one of the characters. The time each child spent reading the story was measured and is summarized in the table below. The study seeks to determine if a child's own name affects attention span.| **Ordinary Story** | | **Own-Name Story** | ||----------------------|---------|---------------------|---------|| **Student** | **Read Time** | **Student** | **Read Time** || A | 2 | G | 7 || B | 3 | H | 10 || C | 7 | I | 11 || D | 9 | J | 4 || E | 6 | K | 12 || F | 7 | | |**Hypothesis Testing at Alpha = 0.05**To test the hypothesis, follow these steps:a) Formulate the null and alternative hypotheses.b) Determine the critical value(s).c) Draw the comparison distribution and shade the rejection region(s).d) Calculate the test statistic using the appropriate formula.e) State the statistical decision based on the test.f) Provide a brief conclusion. This study aims to understand the impact of personalized content on children's reading engagement.

Given information: Student Ordinary story Own Name story A 2.00 G 7 B 3.00 H 10 C…

Answered: 2. An educational psychologist is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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please answer a, b, c
Suppose you were to collect data for the following pair of variables, people: age, grip strength. You want to make a scatterplot. Which variable would you use as the explanatory variable? age grip strength Which variable would you use as the response variable? age grip strength Would you expect to see a positive or negative association? positive negative neither
A marketing firm is doing research for an Internet-based company. It wants to appeal to the age group of people who spend the most money online. The company wants to know if there is a difference in the mean amount of money people spend per month on Internet purchases depending on their age bracket. The marketing firm looked at two age groups, 1818-2424 years and 2525-3030 years, and collected the data shown in the following table. Let Population 1 be the amount of money spent per month on Internet purchases by people in the 1818-2424 age bracket and Population 2 be the amount of money spent per month on Internet purchases by people in the 2525-3030 age bracket. Assume that the population variances are not the same. Internet Spending per Month 1818-2424 Years 2525-3030 Years Mean Amount Spent 65.5765.57 60.1260.12 Standard Deviation 21.6821.68 15.5215.52 Sample Size 1919 1818 Step 1 of 2 : Construct a 90%90% confidence interval for the true difference…
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A marketing firm is doing research for an Internet-based company. It wants to appeal to the age group of people who spend the most money online. The company wants to know if there is a difference in the mean amount of money people spend per month on Internet purchases depending on their age bracket. The marketing firm looked at two age groups, 1818-2424 years and 2525-3030 years, and collected the data shown in the following table. Let Population 1 be the amount of money spent per month on Internet purchases by people in the 1818-2424 age bracket and Population 2 be the amount of money spent per month on Internet purchases by people in the 2525-3030 age bracket. Assume that the population variances are not the same. Internet Spending per Month 1818-2424 Years 2525-3030 Years Mean Amount Spent 50.40 65.33 Standard Deviation 15.85 20.76 Sample Size 17 27 Step 1 of 2 : Construct an 80%80% confidence interval for the true difference between the mean amounts of…
ReAb. a question can influence eyewitness memory. In the study, college students watched a film of ap automobile accident and then were asked questions about what they saw. One group was asked, "About how fast were the cars going when they smashed into each other?" Another group was asked the same question except the verb was changed to "hit" in- stead of "smashed into." The "smashed into" group reported significantly higher estimates of speed than the "hit" group. Suppose a researcher repeats this study with a sample of today's college students and obtains the following results. Estimated Speed Smashed into Hit n 15 n = 15 M = 40.8 M = 34.0 SS = 510 SS = 414 a. Do the results indicate a significantly higher esti- mated speed for the "smashed into" group? Use a one-tailed test with a = .01. b. Compute the estimated value for Cohen's d to measure the size of the effect. the hypothesis test and the measure of effect size would appear in a research report. nort higher 18. In and a classic
If there are 13 data points in a set of data, what is the number of degrees of freedom?
Would you like a cup of tea? Carole and Julius are getting ready to open a new cafe and are gathering up information about sales of different drinks in their state. They obtain data containing the yearly sales (in $1000s) for three types of tea: Darjeeling, Earl Grey, and Green Tea. A boxplot of the data and a histogram of the sales for all three teas combined is shown below. Note: Clicking on any image in this problem will open it in a new window, allowing you to enlarge the view. Tea Sales by Product Combined Tea Sales Darjeeling Earl Grey Green Tea 100 200 300 400 Product Sales in $1000 Part 1: Use the plots above to make quantitative comparisons and answer the following questions: Quantity A: The 75th percentile (Q3) of Sales for Darjeeling Tea Quantity B: The 75th percentile (Q3) of Sales for Green Tea Quantity A is greater 008 007 Frequency 00z 001 Sales in $1000
A marketing firm is doing research for an internet-based company. It wants to appeal to the age group of people who spend the most money online. The company wants to know if there is a difference in the mean amount of money people spend per morith on Internet purchases depending on their age bracket. The marketing firm looked at two age groups, 18-24 years and 25-30 years, and collected the data shown in the following table. Let Population 1 be the amount of money spent per month on internet purchases by people in the 18-24 age bracket and Population 2 be the amount of money spent per month on internet purchases by people in the 25-30 age bracket. Assume that the population variances are not the same. Internet Spending per Month 18-24 Years Answer Mean Amount Spent Standard Deviation Sample Size Step 1 of 2: Construct a 99 % confidence interval for the true difference between the mean amounts of money per month that people in these two age groups spend on Internet purchases. Round the…
How young is too young to have a cell phone? A group of eighth-grade boys and girls were surveyed and asked if they had a cell phone, with the following results. Cell Phone No Cell Phone Boys 54 46 Girls 57 43 (a) Draw a stacked bar chart to describe the data. I Cell Phone I No Cell Phone 1 Cell Phone I No Cell Phone 1 Cell Phone I No Cell Phone Frequency Frequency Frequency 100 100 100 80 80 80 60 60 60 40 40 40 20 20 20 Gender- Gender- Gender Boys Girls Вoys Girls Воys Girls Cell Phone No Cell Phone Frequency 100 80 60 40 20
Would you like a cup of tea? Carole and Julius are getting ready to open a new cafe and are gathering up information about sales of different drinks in their state. They obtain data containing the yearly sales (in $1000s) for three types of tea: Darjeeling, Earl Grey, and Green Tea. A boxplot of the data and a histogram of the sales for all three teas combined is shown below. Note: Clicking on any image in this problem will open it in a new window, allowing you to enlarge the view. Tea Sales by Product Combined Tea Sales Darjeeling Earl Grey Green Tea 100 200 300 400 Product Sales in $1000 Part 1: Use the plots above to make quantitative comparisons and answer the following questions: Quantity A: The 75th percentile (Q3) of Sales for Darjeeling Tea Quantity B: The 75th percentile (Q3) of Sales for Green Tea Quantity A is greater Quantity A: The median of Sales for Darjeeling Tea Quantity B: The median of Sales for Green Tea Quantity B is greater 00€ 007 Frequency > 000 008 007 Sales in…

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