The critical boundaries for a hypothesis test are z = +1.96 and -1.96. If the z-score for the sample data is z = 1.90, then what is the correct statistical decision?Group of answer choicesFail to reject H1Reject H1Fail to reject H0Reject H0
Question
The critical boundaries for a hypothesis test are z = +1.96 and -1.96. If the z-score for the sample data is z = 1.90, then what is the correct statistical decision?Group of answer choicesFail to reject H1Reject H1Fail to reject H0Reject H0
Solution
The correct statistical decision would be to "Fail to reject H0".
Here's why:
The critical boundaries for a hypothesis test are z = +1.96 and -1.96. This means that any z-score that falls within this range would not be considered statistically significant at the 0.05 level (which is what these z-scores represent), and therefore, we would fail to reject the null hypothesis (H0).
In this case, the z-score for the sample data is z = 1.90, which falls within the critical boundaries of -1.96 and +1.96. Therefore, we do not have enough evidence to reject the null hypothesis (H0), so we fail to reject H0.
Similar Questions
A researcher conducts a hypothesis test to evaluate the effect of a treatment that is expected to increase scores. The hypothesis test produces a z-score of z = 2.37. If the researcher is using a one-tailed test, what is the correct statistical decision?Group of answer choicesReject the null hypothesis with α = .05 but not with α = .01.This cannot be answered without additional information.Reject the null hypothesis with either α = .05 or α = .01.Fail to reject the null hypothesis with either α = .05 or α = .01.
A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population. If the researcher uses a one-tailed test with a = .01, then which of the following correctly identifies the critical region?Group of answer choicesz < 2.58z > 2.58z > 2.33z < 2.33
A two-tailed hypothesis test is being used to evaluate a treatment effect with α = .05. If the sample data produce a z-score of z = 2.24, then what is the correct decision?Group of answer choicesFail to reject the null hypothesis and conclude that the treatment has an effect.Fail to reject the null hypothesis and conclude that the treatment has no effect.Reject the null hypothesis and conclude that the treatment has no effect.Reject the null hypothesis and conclude that the treatment has an effect.
In testing the hypothesesH0: μ = 75HA: μ < 75,if the value of the Z test statistic equals -1.78, then the p-value is:Group of answer choices0.9625.0.375.0.5375.0.4625.
The rejection region for testing the hypothesesH0: μ = 100HA: μ ≠100at the 0.05 level of significance is:Group of answer choices|Z| > 1.96.Z < 2.33.|Z < 0.95.Z > 1.65.
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