Inference for Means
About the Lecture
The lecture Inference for Means by David Spade, PhD is from the course Statistics Part 2. It contains the following chapters:
- Inference for Means
- The t-Distribution
- Three Conditions
- Using Margin of Error
- Pitfalls to Avoid
Included Quiz Questions
What describes the central limit theorem?
- The distribution of the sample mean is more normal with larger sample sizes.
- The distribution of the sample mean is more normal with smaller sample sizes.
- In order for the central limit theorem to apply, the population must be normal.
- The standard deviation of the sample mean increases as the sample size increases.
- The distribution of the standard deviation increases with larger sample sizes.
What is not true of the use of the t-distribution as a model for the sample mean?
- The population standard deviation must be known.
- The data must come from a normal population.
- The population standard deviation is estimated with the sample standard deviation.
- The test statistic is computed in the same way as the z-statistic from previous procedures, but the population standard deviation is estimated.
- The data must come from a random sample.
What is not a property of the t-distribution?
- It has thinner tails than the normal distribution.
- It is more peaked than the normal distribution.
- The population's standard deviation is unknown.
- As the degrees of freedom increase, the t-distribution looks more and more like the normal distribution.
- The t-distribution may construct a confidence interval for the true mean.
What is the t-statistic if the hypothesized mean difference is 3, the sample mean difference is 1, the sample standard deviation of the difference is 2, and the sample size is 25?
- 5
- 1
- 3
- 4
- 2
What is not a condition required for a one-sample t-interval for means?
- The larger the sample size, the more unimodal and symmetric the histogram must look in order to use the t-interval.
- The data must come from a random sample.
- The data comes from a distribution that appears to be unimodal and symmetric.
- The sample size must be smaller than 10% of the population size.
- There may not be a strong skew to the data.
What is poor practice when using the one-sample t-procedure?
- It is poor practice to use the one-sample t-procedure with non-randomized data.
- It is poor practice to watch out for outliers.
- One should look for multimodal sets of data.
- It is poor practice to watch out for biased data.
- One should look for skewed data.
What is the t-statistic if the hypothesized mean is 5, sample mean is 3, sample standard deviation is 1, and sample size is 16?
- 8
- 5
- 6
- 7
- 9
For which hypothesis are we likely to use a two-tailed test?
- H1: µ ≠ 5
- H1: µ < 5
- H1: µ > 5
- H1: µ ≤ 5
- H1: µ Δ 5
A t-distribution is used when the population standard deviation is unknown and the sample size is less than what value?
- 30
- 10
- 20
- 40
- 50
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Author of lecture Inference for Means
David Spade, PhD
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