Inference
A researcher wants to estimate the average amount of sleep students at a high school get each night. What type of inference procedure should they use?
A confidence interval for a population mean should be used because the researcher is estimating an average (mean).
If the probability of rain tomorrow is 0.25, what is the probability that it does NOT rain?
0.75
What is the difference between a census and a sample?
A census collects data from every individual in the population, while a sample collects data from only part of the population.
What does a positive association mean in a scatterplot?
A positive association means that as one variable increases, the other variable tends to increase.
What shape does a normal distribution have?
A normal distribution is bell-shaped and symmetric.
A 95% confidence interval for the proportion of students who play sports is (0.42, 0.58). Interpret this interval in context.
We are 95% confident that the true proportion of students at the school who play sports is between 42% and 58%.
A standard deck contains 52 cards. What is the probability of drawing a king?
131
A school surveys every 10th student entering the building. What sampling method is being used?
This is a systematic sample.
What is an outlier in a scatterplot?
An outlier is a point that falls far away from the overall pattern of the data.
In a normal distribution, what percent of data falls within 1 standard deviation of the mean?
About 68% of the data falls within 1 standard deviation of the mean.
A significance test is performed with hypotheses:
H0:p=0.50 Ha:p>0.50
The p-value is 0.03. Interpret this result at the 5% significance level.
Since:
0.03<0.05
The p-value is less than the significance level.
Therefore, we reject H0.
There is convincing evidence that the true proportion is greater than 0.50.
Two dice are rolled. What is the probability that the sum is 8?
365
Explain why voluntary response samples are often biased.
Voluntary response samples are biased because people with strong opinions are more likely to respond, causing underrepresentation of the general population.
A scatterplot shows a strong negative linear relationship. Describe what this means.
As one variable increases, the other variable decreases, and the points lie close to a straight line.
The mean of a normal distribution is 70 and the standard deviation is 5. Find the z-score for a value of 80.
z= 80-70/5 = 2
Final Answer:
2
A random sample of 64 students had a mean test score of 82 with a standard deviation of 16. Find the standard error of the sample mean.
The standard error is 2.
A student guesses randomly on a 5-question true/false quiz. What is the probability they get exactly 4 correct?
0.15625
A researcher divides students into freshmen, sophomores, juniors, and seniors, then randomly samples from each group. What sampling method is this and why is it useful?
This is a stratified random sample.
It is useful because it guarantees representation from each grade level and can reduce variability in the results.
The equation of a least-squares regression line is:
ŷ=2+5x
Predict the value of y when x=4.
Substitute x=4:
ŷ=2+5(4) =2+20 =22
Final Answer:
22
IQ scores are normally distributed with mean 100 and standard deviation 15. What percent of students have an IQ below 115?
z= 115-110/15
z=1
P(Z<1)=0.8413
Final Answer:
About 84.13%
A company claims that 70% of customers are satisfied with their service. A sample of 150 customers found that 93 were satisfied. Perform the hypothesis test at the 0.05 significance level.
Since:
0.032<0.05
reject H0.
There is sufficient evidence that the true satisfaction rate differs from 70%.
A random variable has mean 12 and standard deviation 3. Use the empirical rule to find the interval containing about 95% of values.
About 95% of values are between 6 and 18.
A survey asks: “Don’t you agree that homework should be reduced?” Identify the issue with this question and explain how it could affect results.
This is a leading question because it encourages respondents toward a specific answer.
This could create response bias, making the survey results less reliable because participants may feel pressured to agree.
A student found a correlation of r=0.92 between study time and test scores. What does this tell us, and why does it NOT prove causation?
A correlation of:
r=0.92
indicates a very strong positive linear relationship between study time and test scores.
However, correlation does not prove causation because other variables may influence the relationship, such as prior knowledge, tutoring, or motivation.
Heights of adult males are normally distributed with mean 69 inches and standard deviation 2.5 inches. Find the height that marks the top 10%.
Top 10% means:
P(Z<z)=0.90
Using invNorm:
z≈1.28
Now solve for height:
x=69+1.28(2.5)
x=69+3.2
x=72.2
Final Answer:
About 72.2 inches