An experimenter conducted a two-tailed hypothesis test on a set of data and obtained a p-value of 0.44. If the experimenter had conducted a one-tailed test on the same set of data, which of the following is true about the possible p-value(s) that the experimenter could have obtained? A) The only possible p-value is 0.44. B) The only possible p-value is 0.88. C) The possible p-values are 0.22 and 0.78. D) The possible p-values are 0.22 and 0.88.

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warylucknow warylucknow · Answer 1 · 2020-02-19T07:25:35+01:00

Answer:

Correct option is (C).

The possible value of the p-value for a one-tailed test are 0.22 and 0.78.

Step-by-step explanation:

The p-value is the probability of acquiring a result as extreme as the observed result, assuming the null hypothesis statement is true.

The p value of a test is:

Left-tailed test: [tex]P(TS<ts)[/tex]

Right-tailed test: [tex]P(TS>ts) = 1- P(TS<ts)[/tex].

Here,

TS = Test statistic

ts = computed value of the test statistic.

The two-tailed p-value is: [tex]2P(TS<ts)[/tex] or [tex]2P(TS>ts)[/tex].

The p-value of the two tailed test is, 0.44.

Compute the p-value for one-tailed test a follows:

[tex]2P(TS<ts)=0.44\\P(TS<ts)=\frac{0.44}{2}\\ =0.22[/tex]

[tex]P(TS>ts) = 1- P(TS<ts)\\=1-0.22\\=0.78[/tex]

Thus, the possible value of the p-value for a one-tailed test are 0.22 and 0.78.

The correct option is (C).