Question

1.(a) Find the p-value of the following test given that

x̅ = 990, n = 100 and σ = 25.

H0 : μ >= 1000

Ha : μ < 1000

(b) Repeat part (a) with σ = 50.

(c) Repeat part (a) with σ = 100.

(d) Suppose the significance level is 0.05, what will be your conclusion to parts (a), (b) and (c)?

Answer 1

(a)

We use Excel function "NORMSDIST()" as :

(b)

We use Excel function "NORMSDIST()" as :

(c)

We use Excel function "NORMSDIST()" as :

(d)

Conclusion to part (a) :

Since P-value = 0 < 0.05, we reject the null hypothesis Ho

Conclusion to part (b) :

Since P-value = 0.0228 < 0.05, we reject the null hypothesis Ho

Conclusion to part (c) :

Since P-value = 0.1587 > 0.05, we do not reject the null hypothesis Ho