Question

# A population is normal with a mean of 80 and a standard deviation of 12. A...

A population is normal with a mean of 80 and a standard deviation of 12.
A simple random sample of 50 is selected from the population. The sample mean is 78. What is the p-value if you are conducting a lower-tail (left tail) test?

Solution :

Null and alternative hypotheses :

The null and alternative hypotheses would be as follows :

Test statistic :

To test the hypothesis the most appropriate test is one sample z-test for mean. The test statistic is given as follows :

Where, x̅ is sample mean, μ is hypothesized value of population mean under H​​​​​​0, σ is population standard deviation and n is sample size.

We have,  x̅ = 78, μ = 80, n = 50 and  σ = 12

The value of the test statistic is -1.1785.

P-value :

For left-tailed z-test the p-value is given as follows :

P-value = P(Z < value of the test statistic)

P-value = P(Z < -1.1785)

P-value = 0.1193

The p-value is 0.1193.

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