PORTAGE LEARNING STATISTICS MODULE 4, Exams of Statistics

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1. What is the alternative hypothesis ((H_a))? Answer: A statement that a significant difference or effect exists. Rationale: The alternative hypothesis is supported when evidence against the null hypothesis is strong enough.
2. For a two-tailed z-test at (\alpha = 0.05), what are the critical z-values? Answer: [ \pm1. ] Rationale: Any z-score beyond ±1.96 falls in the rejection region.
3. If a calculated z-score equals 2.45 in a two-tailed test with (\alpha = 0.05), what decision should be made? Answer: Reject the null hypothesis. Rationale: Since 2.45 > 1.96, the z-score falls in the rejection region.
4. What is a Type I error? Answer: Rejecting a true null hypothesis. Rationale: This is a "false positive" conclusion.
5. What is the standard error when (\sigma = 20) and (n = 25)? Answer:

[

SE=\frac{\sigma}{\sqrt{n}} =\frac{20}{5} = ] Rationale: The standard error estimates the variability of sample means.

1. A z-test produces a p-value of 0.03. At (\alpha = 0.05), what is the decision? Answer: Reject the null hypothesis. Rationale: Since (0.03 < 0.05), the result is statistically significant.
2. When is a z-test preferred over a t-test? Answer: When the population standard deviation is known and the sample is sufficiently large. Rationale: The z-test relies on knowledge of the population standard deviation, whereas the t-test is used when it is unknown.