Question

A company that produces garden hoses claims their product has a lifespan of at least 20 years. Thus, they came up with the following hypothesis test.

H0 : μ ≥ 20
Ha : μ < 20

A sample of 50 garden hoses provided a mean lifespan of 19.4 years, with a (population) standard
deviation of 2.

(a) Compute the z-value test statistic

B) what is the p-value?

c) Using α = 0.05, do you Reject H0 or Fail to reject H0?

Answer 1

(a) z-value = -2.12

(b) p-value = 0.0170

(c) Reject H0

Explanation:

(a)

`std-err=(std-dev)/(√(n))=(2)/(√(50))=0.2828`

`z-value=(X-mean)/(std-err)=(19.4-20)/(0.2828)=-2.12`

(b)

with

z-value = -2.12

significance level = 0.05

one-tail hypothesis (H0: μ ≥ 20)

We can see on the normal distribution table (Z-Score table) that

p-value = 0.0170

(c)

Since p value (0.0170) is less than α=0.05 we reject H0

Hope this helps!