136 Finding pvalue a a 005 TS 1635 twotailed ztest b a 00

13-6. (Finding p-value) a. a = 0.05, TS = -1.635, two-tailed z-test b. a = 0.01, TS = 3.145, lower-tailed t-test, n=100 c. a = 0.1, TS = - 2.107, two-tailed t-test, n = 27

Solution

a)

We first find the left tailed area of this negative z score, then multiply it by 2 (as it is 2 tailed).

Using technology,

P(z<-1.635) = 0.051024524

Hence, the two tailed area is

P value = 0.102049048 [ANSWER]

And so P > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS.

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b)

Using technology, (like TDIST function in Excel) with df = n - 1 = 99, one tailed, the left tailed area of TS = 3.145 is

P = 0.998903431 [ANSWER]

[Could you please check if it is -3.145 instead? In that case, P = 0.001096569. In that case we reject the null hypothesis as P < 0.01.]

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c)

Using technology, (like TDIST function in Excel) with df = n - 1 = 26, two tailed,

P = 0.044918413 [ANSWER]

[So, we reject the null hypothesis as P < 0.1]