Question

A certain factory consumes on average 1000 litres of water per day with a variance (σ2) of 625 litres2. A random sample of 100 days taken revealed a mean daily consumption of x ̅ = 1006 litres. At α = 0.01, test if the mean daily water intake remains 1000 litres against the alternative that the mean water consumption has changed. please provide clear explaination

a) Hypotheses:

b) Rejection Region:

c) Test Statistic:

d) Decision/Conclusion:

Answer 1

This is the two tailed test .

The null and alternative hypothesis is

H₀ : = 1000

H_a : 1000

Test statistic = z

= ( - ) /    / n

= (1006 - 1000) / 25 / 100

Test statistic = 2.4

Rejection region = -2.576 , +2.576

Fail to reject the null hypothesis .

There is insufficient evidence to conclude that the mean water consumption has changed.