A researcher is testing a hypothesis of a single mean. The critical z value for a = .05 and a two‑tailed test is +1.96. The observed z value from sample data is ‑2.05. The decision made by the researcher based on this information is to the null hypothesis.

The decision made by the researcher based on this information is to reject the null hypothesis.

Step-by-step explanation:

Two-tailed hypothesis test:

Critical value:

Test statistic: z

If , we do not reject the null hypothesis.

If , we reject the null hypothesis.

In this question:

Since , we reject the null hypothesis.

The decision made by the researcher based on this information is to reject the null hypothesis.

ratio is 2 : 9

the answer is three

13.5 : 3

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