Question

In testing the hypotheses H 0 colon space mu space equals space 800 space v s. space H 1 colon space mu not equal to space 800, if the value of the test statistic equals 1.75, then the p-value is:

Answer 1

The p-value is 0.0802.

Explanation:

The hypothesis for a test is defined as:

H₀: μ = 800 vs. Hₐ: μ ≠ 800

A two tailed test for the population mean can be performed using a z-test or a t-test.

A z-test is used if the data provided has information related to the population standard deviation and the sample size is large, i.e. n > 30.

And if the population standard deviation is not known and the sample size is small, then the t-test will be used.

Since there is no information about either the population standard deviation or the sample size, assume that z-test is used.

The test statistic value is:

z = 1.75

Compute the p-value of the test as follows:

`p-value=2* P(Z>z)\\`

`=2* (1-0.9599)\\=2* 0.0401\\=0.0802`

*Use a z-table for the probability.

Thus, the p-value is 0.0802.