Two Population Means with Known Standard Deviations Quiz
The question sheet
Reveal any answer as you study-
For two independent means with known population standard deviations, what is the random variable?
- X̄1 – X̄2
- X̄1 ÷ X̄2
- X̄1 + X̄2
- X̄1 × X̄2
Reveal answer
Answer: X̄1 – X̄2
Source evidence
PDF page 600: Even though this situation is not likely (knowing the population standard deviations), the following example illustrates hypothesis testing for independent means, known population standard deviations. The sampling distribution for the ̄ ̄ difference between the means is normal, and both populations must be normal. The random variable is X – X . The 1 2 normal distribution has the following format: Normal distribution is ⎡
PDF page 601: Solution 10.6 This is a test of two independent groups, two population means, population standard deviations known. ̄ ̄ Random Variable: X – X = difference in the mean number of months the competing floor waxes last. 1 2
-
When population standard deviations are known, the sampling distribution for the difference between means is:
- Normal
- Binomial
- Uniform
- Exponential
Reveal answer
Answer: Normal
Source evidence
PDF page 600: Even though this situation is not likely (knowing the population standard deviations), the following example illustrates hypothesis testing for independent means, known population standard deviations. The sampling distribution for the ̄ ̄ difference between the means is normal, and both populations must be normal. The random variable is X – X . The 1 2 normal distribution has the following format: Normal distribution is ⎡
-
For the known-standard-deviations test, both populations must have what type of distribution?
- Uniform
- Bimodal
- Skewed
- Normal
Reveal answer
Answer: Normal
Source evidence
PDF page 600: Even though this situation is not likely (knowing the population standard deviations), the following example illustrates hypothesis testing for independent means, known population standard deviations. The sampling distribution for the ̄ ̄ difference between the means is normal, and both populations must be normal. The random variable is X – X . The 1 2 normal distribution has the following format: Normal distribution is ⎡
-
In the floor wax test, at 5% significance, what decision was made?
- Do not reject H0
- Reject H0
- Accept Ha
- Cannot decide
Reveal answer
Answer: Do not reject H0
Source evidence
PDF page 601: 1 2 Compare α and the p value: α = 0.05 and p value = 0.1799. Therefore, α < p value. Make a decision: Since α < p value, do not reject H0. Conclusion: At the 5 percent level of significance, from the sample data, there is not sufficient evidence to conclude that the mean time Wax 1 lasts is longer (Wax 1 is more effective) than the mean time Wax 2 lasts.
-
In the floor wax example, what was the calculated p value?
- 0.4040
- 0.1799
- 0.9157
- 0.05
Reveal answer
Answer: 0.1799
Source evidence
PDF page 601: Calculate the p value using the normal distribution: p value = 0.1799 Graph:
-
In the floor wax test, what is the value of X̄1 – X̄2?
- 0.33
- 2.9
- 0.1
- 3.0
Reveal answer
Answer: 0.1
Source evidence
PDF page 601: X – X = 3 – 2.9 = 0.1
-
Because Wax 1 'is more effective,' which symbol goes into Ha?
- =
- <
- ≠
- >
Reveal answer
Answer: >
Source evidence
PDF page 601: The words is more effective says that Wax 1 lasts longer than Wax 2, on average. Longer is a > symbol and goes into Ha. Therefore, this is a right-tailed test. Distribution for the test: The population standard deviations are known, so the distribution is normal. Using the formula, the distribution is 2
-
The phrase 'is more effective' makes the floor wax test which type?
- No tail
- Left-tailed
- Right-tailed
- Two-tailed
Reveal answer
Answer: Right-tailed
Source evidence
PDF page 601: The words is more effective says that Wax 1 lasts longer than Wax 2, on average. Longer is a > symbol and goes into Ha. Therefore, this is a right-tailed test. Distribution for the test: The population standard deviations are known, so the distribution is normal. Using the formula, the distribution is 2
-
Since μ1 ≤ μ2, the mean for the normal distribution used in the test is:
- One
- 0.33
- 0.05
- Zero
Reveal answer
Answer: Zero
Source evidence
PDF page 601: Since μ1 ≤ μ2, then μ1 – μ2 ≤ 0 and the mean for the normal distribution is zero.
-
In the floor wax test, what was the test statistic (z-score)?
- 0.9157
- 0.1799
- 0.4040
- 0.05
Reveal answer
Answer: 0.9157
Source evidence
PDF page 601: Press STAT. Arrow over to TESTS and press 3:2-SampZTest. Arrow over to Stats and press ENTER. Arrow down and enter .33 for sigma1, .36 for sigma2, 3 for the first sample mean, 20 for n1, 2.9 for the second sample mean, and 20 for n2. Arrow down to μ1: and arrow to > μ2. Press ENTER. Arrow down to Calculate and press ENTER. The p value is p = 0.1799, and the test statistic is 0.9157. Do the procedure again, but instead of Calculate do Draw.
-
Which calculator command is used for the floor wax test?
- 2-SampZTest
- 1-SampZTest
- 2-SampTTest
- Z-Interval
Reveal answer
Answer: 2-SampZTest
Source evidence
PDF page 601: Press STAT. Arrow over to TESTS and press 3:2-SampZTest. Arrow over to Stats and press ENTER. Arrow down and enter .33 for sigma1, .36 for sigma2, 3 for the first sample mean, 20 for n1, 2.9 for the second sample mean, and 20 for n2. Arrow down to μ1: and arrow to > μ2. Press ENTER. Arrow down to Calculate and press ENTER. The p value is p = 0.1799, and the test statistic is 0.9157. Do the procedure again, but instead of Calculate do Draw.
-
In the senators example, what was the calculated p value?
- 0.1799
- 0.05
- 0.9157
- 0.4040
Reveal answer
Answer: 0.4040
Source evidence
PDF page 602: Calculating the p value using the normal distribution gives p value = 0.4040. Graph:
High School Statistics
High School Statistics by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
Make your own — free
Turn any notes into a game in under a minute. Free to start.