Question

Suppose H0: mu = 120 is tested against H1: mu > 120 with known variance 10 and n = 25. What p-value corresponds to a sample mean ybar = 121.5

Answer 1

Solution:

The null and alternative hypotheses are as follows:

To test the hypothesis we shall use z-test for single mean. The test statistic is given as follows:

Where, where, is sample mean, is population variance, n is sample size and is hypothesized value of population mean under H​​​​​​0.

We have,

The value of the test statistic is 2.3717.

Since, our test is right-tailed test, therefore we shall obtain right-tailed p-value for the test statistic. The right-tailed p-value is given as follows:

p-value = P(Z > value of the test statistic)

p-value = P(Z > 2.3717)

Using "pnorm" function of R we get, P(Z > 2.3717) = 0.0089

Hence, p-value= 0.0089

The p-value is 0.0089.

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