Exam 21: Univariate Statistical Analysis

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When sample size (n) is larger than _____, the t-distribution and Z-distribution are almost identical.

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D

Define one- and two-tailed univariate tests and describe when each is appropriate. Give an example hypothesis that can be tested with each test.

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A one-tailed univariate test is appropriate when the researcher has a directional hypothesis implying that an observed mean can only be greater than or less than a hypothesized value. Thus, only one of the "tails" of the bell-shaped normal curve is relevant. For example, the following hypothesis could be appropriately examined with a one-tailed test:
H1: The number of fast food restaurants within the 71201 zip code is greater than five.
A two-tailed test is one that tests for differences from the population mean that are either greater or less. Thus, the extreme values of the normal curve (or tails) on both the right and the left are considered. In practical terms, when a research question does not specify whether a difference should be greater than or less than, a two-tailed test is most appropriate. For example, the following hypothesis could be examined using a two-tailed test:
H2: The number of fast food restaurants within the 71201 zip code is not equal to five.

The critical probability associated with a statistical hypothesis test that indicates how likely it is that an inference supporting a difference between an observed value and some statistical expectation is true is called _____.

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significance level

Suppose that a group of 100 consumers are asked to rate how much they liked the taste of a new soft drink on a 5-point scale (where 5 = good taste and 1 = poor taste) and the mean rating was 4.2 with a standard deviation of 1.48. Suppose, further, that the standard error of the mean for this study was 0.15. If you wanted to find the 95 percent confidence interval (two-tailed test), and if the Z-value at the 0.05 level of significance is 1.96, the confidence interval lies between _____.

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A hypothesis test of a proportion is conceptually similar to hypothesis testing when the mean is the characteristic of interest.

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Compare and contrast significance levels and p-values.

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A statement which expresses the opposite of the null hypothesis is called the ______ hypothesis.

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Compare and contrast parametric statistics and nonparametric statistics.

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The t-distribution has a mean of ______ and a standard deviation of ______.

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The symmetrical, bell-shaped distribution that has a mean of zero and a standard deviation of one is called the ______.

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Univariate statistical analysis tests hypotheses involving only one variable.

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Which of the following is the key indicator of whether or not a hypothesis can be supported?

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Multivariate statistic analyses require five or more variables.

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Nominal scales typically use parametric statistical tests.

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The researcher using sampling runs the risk of committing two types of errors: Type I and Type II errors.

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For which statistical test does the formula given below apply? For which statistical test does the formula given below apply?

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The appropriate test to use when testing hypotheses involving an observed mean against some specified value is the univariate ______ .

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The error caused by failing to reject the null hypothesis when, in fact, the alternative hypothesis is true is called a(n) ______ error.

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Which of the following tests is conceptually similar to the one used when the mean is the characteristic of interest but that differs in the mathematical formulation of the standard error of the proportion?

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Suppose that past research studies have found that 70 percent of a particular target market segment were aware of the Nike "swoosh" brand mark. If 65 percent of this target market in a sample of 60 people are aware of this brand mark, and if the standard error of the proportion is 0.06, the observed Z-test value is approximately _____.

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