Question

Participants in an exercise experiment are asked to rate how difficult a hill-climbing challenge would be when they are rested. A month later, participants are asked to rate how difficult a hill-climbing challenge would be after they have run on a treadmill to exhaustion. The researcher wants to know if people judge hypothetical physical tasks as being more difficult if they are already tired. Assume the rating scale provides interval data that ranges from 0 – very easy to 10 – very difficult. Use the data below to answer the researcher’s question. Assume a two-tailed test with alpha = .05. Provide answers to each of the questions below the table; you must show your work to earn credit.

Participant	Perceived difficulty when rested	Perceived difficulty when tired
1	2	6
2	0	1
3	5	4
4	7	7
5	5	10
6	2	7
7	5	8
8	1	9
9	3	8
10	6	6

1. Calculate M_D

2. Calculate SS

3. What values should appear in the numerator for your t-statistic formula? (provide the actual numbers, not the names)

4. What value should appear in the denominator of your t-statistic formula? (provide the actual number, not the name)

5. Write the outcome of the statistical test as you would in an APA style report. Be sure to include a description of the finding, descriptive statistics, and the result of the statistical test. You do not need to report effect size or confidence intervals.

6. What is the take home message based on these data? Does feeling tired impact the predictions people make about how difficult another physical task would be?   

A researcher is investigating the effectiveness of a new medication for lowering blood pressure for individuals with high systolic pressure (e.g., greater than 136). For this population, systolic scores average µ = 158 with a standard deviation of σ = 20, and the scores are from a normal-shaped distribution. The researcher plans to select a sample of n = 30 individuals, and measure their systolic blood pressure after they take the medication for 60 days. The researcher uses a two-tailed test with alpha = .05. What is the power of the test if the medication has a 7-point effect?

You must show your work to earn credit. I recommend showing each step you go through when calculating power.

7. What is the power of the test if the medication has a 7-point effect?

Answer 1

Given sample data:

X1 <- c(2,0,5,7,5,2,5,1,3,6)
X2 <- c(6,1,4,7,10,7,8,9,8,6)

We have to test (Left tailed T-test)

$H_0:\mu _1-\mu _2\geqslant 0\\ H_1:\mu _1-\mu _2 <0$

Or we can write if   $\mu _1-\mu _2=\mu _D$
$H_0:\mu _D\geqslant 0\\ H_1:\mu _D<0$

1) The sample means are $\overline{x_1}=3.6$ , $\overline{x_2}=6.6$ . The sample standard deviations are Sample sizes are $n_1=10,n_2=10$ .

The estimated mean difference is $\overline{x_1}-\overline{x_2}=-3$

2)The standard deviation/error of the differences of means is $\sqrt{\frac{s _1^2}{n_1}+\frac{s_2^2}{n_2}}=\sqrt{\frac{2.319^2}{10}+\frac{2.59^2}{10}}=1.099495$
3) We use T distribution since the sample sizes are small. The test statistic

$t=\left (\overline{x_1}-\overline{x_2} \right )/\sqrt{\frac{s _1^2}{n_1}+\frac{s _2^2}{n_2}}$

4)The denominator is and the numerator is

5) The statistics is $t=-3/1.0995=-2.728525$

The P-value is $P\left ( T<t \right )=P\left (T<-2.728525 \right )={\color{Blue} 0.0069}$

Sinc the P-value $\textup{P-value} = 0.0069<0.05$ , we reject the null hypothesis

The conclusion is people judge hypothetical physical tasks as being more difficult if they are already tired.

We are required to solve only 4 parts. Please post the remaining questions as another post.