Correlation and Prediction
A researcher wants to investigate if there is a relationship between screen time (X) and presence of an Alzheimer's biomarker (Y). They poll a number of patients with a predisposition of Alzheimer’s on their screen time usage and compare it to their biomarker bloodwork.
X
1
2
2
3
Y
1
2
3
6
Construct a regression equation to predict Y from X. What is the predicted Y for a value of 4?
8
After analyzing her data, a researcher calculates a confidence interval. What new information does the CI provide?
A. How big of an effect the IV had on the DV
B. The upper and lower boundaries between which the researcher is reasonably sure the true population parameters lie
C. Whether the independent variable caused a significant change in scores.
B
A nutritionist claims that a new diet plan results in an average weight loss of 10 pounds after 6 weeks. You want to test this claim.
A random sample of 12 participants who followed the diet shows the following weight losses (in pounds):
Sample data:
8, 12, 9, 14, 7, 10, 11, 6, 13, 9, 8, 12
Assume weight loss is approximately normally distributed.
Conduct a one-sample t-test at the 0.05 significance level to test the claim that the mean weight loss is 10 pounds.
t ≈ –0.12
df = n − 1 = 11
Critical t ≈ ±2.201
Fail to reject H₀: The data suggest that the true mean weight loss does not differ from 10 pounds. There is not enough evidence at the 0.05 significance level to conclude that the true mean weight loss differs from 10 pounds.
Two-tailed test, t = 1.736, df ≈ 6. Find p-value
Decision
α = 0.05
p = 0.13 > 0.05
Fail to reject H₀
Calculate the SEoE (Standard Error of Estimate) for the regression line
A researcher wants to investigate if there is a relationship between screen time (X) and presence of an Alzheimer's biomarker (Y). They poll a number of patients with a predisposition of Alzheimer’s on their screen time usage and compare it to their biomarker bloodwork.
X
1
2
2
3
Y
1
2
3
6
2.449
To compare customer satisfaction levels of two competing cable television companies, 174 customers of Company 1 and 355 customers of Company 2 were randomly selected and were asked to rate their cable companies on a five-point scale, with 1 being least satisfied and 5 most satisfied. The survey results are summarized in the following table:
Company 1:
n1=174
x̄1=3.51
s1=0.51
Company 2:
n2 = 355
x̄2 = 3.24
s2=0.52
Find the point estimate.
x̄1−x̄2 = 3.51−3.24=0.27.
A researcher wants to know whether a short mindfulness exercise reduces stress.
She measures stress level (1–10 scale) before and after the exercise for 6 people.
Person Before After
1 6 5
2 7 6
3 5 4
4 8 6
5
Conduct a paired t-test, α = 0.05, to see if stress decreases.
Decision rule: with df of n-1 = 4, right-tailed test, alpha = .05, reject H_0 when t is more than 2.353
Interpretation
The data suggest that the stretching routine reduces muscle tension.
A candy company claims that the mean weight of its chocolate bars is 50 grams.
A consumer group believes the bars weigh less than advertised.
They randomly sample 9 chocolate bars and obtain these weights (in grams):
49, 47, 50, 48, 46, 49, 47, 48, 47
Assume the weights are normally distributed.
Identify the p-value.
one-sample t-test
p<0.001
Calculate Pearson’s r for the following set of numbers:
X
1
3
4
6
Y
8
5
7
4
r = -.789
sample of apples has weights (in grams) given below.
Find a 95% confidence interval for the mean weight of this kind of apple.
123.7 < μ < 148.5
Ackerman and Goldsmith (2011) found that students who studied text from printed hardcopy had better test scores than students who studied from text presented on a screen. In a related study, a professor noticed that several students in a large class had purchased the e-book version of the course textbook. For the final exam, the overall average for the entire class was μ = 81.7 but the n=9 students who used e-books had a mean of M = 77.2 with a standard deviation of s = 5.7.
Is the sample sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class? Use a two-tailed test with α= .05
The data show that scores for students with e-books are significantly different from scores from the regular class
A light bulb manufacturer claims that its bulbs last an average of 1,000 hours.
A consumer group tests 36 bulbs and finds a sample mean lifetime of 980 hours with a known population standard deviation of 60 hours.
Test at α = 0.05 whether the bulbs last less than claimed.
Given:
H₀: μ = 1,000
H₁: μ < 1,000
n = 36
x̄ = 980
σ = 60
Standard error:
10
z-statistic:
−2
p≈0.0228