Math 110 Chapter 7, 8, 9 Latest Update 2025-2026 70 Questions and 100% Verified Correct Answers Guaranteed A+
Alternate Hypothesis (H1) - CORRECT ANSWER: This is the statement you will adopt in the situation in which the evidence (data) is so strong that you reject H0. A statistical test is designed to assess the strength of the evidence (data) against the null hypothesis.
Assessing Normality - CORRECT ANSWER: We will reject the assumption that a
population is approximately normal if a sample has any of the following features:
- The sample contains an outlier
- The sample exhibits a large degree of skewness
- The sample has more than 1 distinct mode
Assumptions for a Population Proportion Confidence Interval - CORRECT ANSWER: 1) We have a Simple Random Sample (SRS)
2) The Population is at least 20 times as large as the sample
3) The items in the population are divided into two categories
4) The sample must contain at least 10 individuals in each categories
Assumptions for Hypothesis Tests about Proportions - CORRECT ANSWER: 1. SRS
- The population is at least 10x the size of the sample (n≤0.05N)
- The item in the population is divided into 2 categories 1 / 3
- The values np0 and n(1-p0) are both at least 10 (n*p & n*(1-p) ≥ 10)
Central Limit Theorem Rule of Thumb - CORRECT ANSWER: The distribution may be
approximated with a normal curve whenever n*p and n*(1-p) are both at least 10.
Checking a Confidence Interval with Population Standard Deviation known - CORRECT ANSWER: Stat -> Tests -> 7: ZInterval -> Stats ->Input Data
Chi-Square (χ2) Distribution Characteristics - CORRECT ANSWER: 1. The χ2
Distributions are not symmetric. They are skewed to the right
- Values of the χ2 statistic are always greater or equal to zero. They are never
negative.
Conclusions to Hypotheses tests - CORRECT ANSWER: If:
If H0 is rejected, then we can conclude that H1 is true.
If H0 is NOT rejected, then we can conclude that there is not evidence to conclude that H1 is true.
NOTE: This does not mean that the null hypothesis is true, but that the null hypothesis MIGHT be true.
Confidence Interval - CORRECT ANSWER: x̄ - m < μ < x̄ + m
Point Estimate - Margin of Error < Mean (Mu) < Point Estimate + Margin of Error
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Confidence Interval Assumptions for a Population Mean, σ Known - CORRECT
ANSWER: 1) We have a simple random sample (SRS)
2) The sample size is large enough (n>30) to apply Central Limit Theorem or the population is approximately normal.
Confidence Intervals when Population Standard Deviation is Unknown - CORRECT
ANSWER: We use a Student's t distribution
Since we no longer have the standard deviation, we cannot use Zα/2. We must now use tα/2.
Construct Confidence Intervals for a Population Mean when the Population Standard Deviation is Unknown - CORRECT ANSWER: Step 1: Check the assumptions and if it passes, Input all of the data into stats
Step 2: Go to 1-Var Stats and find the Sample mean x̄ and the sample standard
deviation s.
Step 3: Find the degrees of freedom (df=n-1) and the critical value tα/2.
Step 4: Compute the standard error s/√n and multiply it by the critical value to get the margin of error
Step 5: Construct the Confidence Interval
Constructing a Confidence Interval for a Chi-Square distribution - CORRECT ANSWER:
Population Variance:
[(n-1)s^2]/χ2(α/2) < σ2 < [(n-1)s^2]/χ2(1-α/2)
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