Question

A city office in Florida claims that an industrial plant discharge greater than 1000 gallons of wastewater per hour in the neighboring lake. To test this claim seven random sample are taken which showed sample mean as 1300. Let the population standard deviation is known to be 422. What is the p-value? (use Z-table)

Answer 1

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

H0: µ = 1000 versus Ha: µ > 1000

This is an upper tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 1000

Xbar = 1300

σ = 422

n = 7

α = 0.05

Critical value = 1.6449

(by using z-table or excel)

Z = (1300 - 1000)/[422/sqrt(7)]

Z = 1.8809

P-value = 0.0300

(by using Z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that an industrial plant discharge greater than 1000 gallons of wastewater per hour in the neighboring lake.